Algebra InputsTrigonometry InputsCalculus InputsMatrix Inputs Basic algebra trigonometry calculus statistics matrices CharactersSolve for n n=-\frac{3\left(25c^{2}+1\right)}{2c\left(1-75c\right)} c\neq \frac{1}{75}\text{ and }c\neq 0View solution stepsSteps for Solving Linear Equation 5 c - \frac { 25 c ^ { 2 } + 1 } { 10 n c } = \frac { 1 } { 15 } Variable n cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 30cn, the least common multiple of 10nc,15. 5c\times 30cn-3\left(25c^{2}+1\right)=2cn Multiply 5 and 30 to get 150. 150ccn-3\left(25c^{2}+1\right)=2cn Multiply c and c to get c^{2}. 150c^{2}n-3\left(25c^{2}+1\right)=2cn Use the distributive property to multiply -3 by 25c^{2}+1. 150c^{2}n-75c^{2}-3=2cn Subtract 2cn from both sides. 150c^{2}n-75c^{2}-3-2cn=0 Add 75c^{2} to both sides. Anything plus zero gives itself. 150c^{2}n-3-2cn=75c^{2} Add 3 to both sides. 150c^{2}n-2cn=75c^{2}+3 Combine all terms containing n. \left(150c^{2}-2c\right)n=75c^{2}+3 Divide both sides by 150c^{2}-2c. \frac{\left(150c^{2}-2c\right)n}{150c^{2}-2c}=\frac{75c^{2}+3}{150c^{2}-2c} Dividing by 150c^{2}-2c undoes the multiplication by 150c^{2}-2c. n=\frac{75c^{2}+3}{150c^{2}-2c} Divide 75c^{2}+3 by 150c^{2}-2c. n=\frac{3\left(25c^{2}+1\right)}{2c\left(75c-1\right)} Variable n cannot be equal to 0. n=\frac{3\left(25c^{2}+1\right)}{2c\left(75c-1\right)}\text{, }n\neq 0 Solve for c \left\{\begin{matrix}c=\frac{\sqrt{n^{2}+450n-225}+n}{75\left(2n-1\right)}\text{; }c=\frac{-\sqrt{n^{2}+450n-225}+n}{75\left(2n-1\right)}\text{, }&\left(n\neq \frac{1}{2}\text{ and }n\geq 15\sqrt{226}-225\right)\text{ or }n\leq -15\sqrt{226}-225\\c=-3\text{, }&n=\frac{1}{2}\end{matrix}\right.QuizAlgebra5 problems similar to: 5 c - \frac { 25 c ^ { 2 } + 1 } { 10 n c } = \frac { 1 } { 15 }
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CopyCopied to clipboard5c\times 30cn-3\left(25c^{2}+1\right)=2cn Variable n cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 30cn, the least common multiple of 10nc,15.150ccn-3\left(25c^{2}+1\right)=2cn Multiply 5 and 30 to get 150.150c^{2}n-3\left(25c^{2}+1\right)=2cn Multiply c and c to get c^{2}.150c^{2}n-75c^{2}-3=2cn Use the distributive property to multiply -3 by 25c^{2}+1.150c^{2}n-75c^{2}-3-2cn=0 Subtract 2cn from both sides.150c^{2}n-3-2cn=75c^{2} Add 75c^{2} to both sides. Anything plus zero gives itself.150c^{2}n-2cn=75c^{2}+3 Add 3 to both sides.\left(150c^{2}-2c\right)n=75c^{2}+3 Combine all terms containing n.\frac{\left(150c^{2}-2c\right)n}{150c^{2}-2c}=\frac{75c^{2}+3}{150c^{2}-2c} Divide both sides by 150c^{2}-2c.n=\frac{75c^{2}+3}{150c^{2}-2c} Dividing by 150c^{2}-2c undoes the multiplication by 150c^{2}-2c.n=\frac{3\left(25c^{2}+1\right)}{2c\left(75c-1\right)} Divide 75c^{2}+3 by 150c^{2}-2c.n=\frac{3\left(25c^{2}+1\right)}{2c\left(75c-1\right)}\text{, }n\neq 0 Variable n cannot be equal to 0.
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View solution stepsSteps for Solving Linear Equation 5 c - \frac { 25 c ^ { 2 } + 1 } { 10 n c } = \frac { 1 } { 15 } Variable n cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 30cn, the least common multiple of 10nc,15. 5c\times 30cn-3\left(25c^{2}+1\right)=2cn Multiply 5 and 30 to get 150. 150ccn-3\left(25c^{2}+1\right)=2cn Multiply c and c to get c^{2}. 150c^{2}n-3\left(25c^{2}+1\right)=2cn Use the distributive property to multiply -3 by 25c^{2}+1. 150c^{2}n-75c^{2}-3=2cn Subtract 2cn from both sides. 150c^{2}n-75c^{2}-3-2cn=0 Add 75c^{2} to both sides. Anything plus zero gives itself. 150c^{2}n-3-2cn=75c^{2} Add 3 to both sides. 150c^{2}n-2cn=75c^{2}+3 Combine all terms containing n. \left(150c^{2}-2c\right)n=75c^{2}+3 Divide both sides by 150c^{2}-2c. \frac{\left(150c^{2}-2c\right)n}{150c^{2}-2c}=\frac{75c^{2}+3}{150c^{2}-2c} Dividing by 150c^{2}-2c undoes the multiplication by 150c^{2}-2c. n=\frac{75c^{2}+3}{150c^{2}-2c} Divide 75c^{2}+3 by 150c^{2}-2c. n=\frac{3\left(25c^{2}+1\right)}{2c\left(75c-1\right)} Variable n cannot be equal to 0. n=\frac{3\left(25c^{2}+1\right)}{2c\left(75c-1\right)}\text{, }n\neq 0 Solve for c \left\{\begin{matrix}c=\frac{\sqrt{n^{2}+450n-225}+n}{75\left(2n-1\right)}\text{; }c=\frac{-\sqrt{n^{2}+450n-225}+n}{75\left(2n-1\right)}\text{, }&\left(n\neq \frac{1}{2}\text{ and }n\geq 15\sqrt{226}-225\right)\text{ or }n\leq -15\sqrt{226}-225\\c=-3\text{, }&n=\frac{1}{2}\end{matrix}\right.
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