Solve x/7-x^5/5+c/4x^4=y

$$\frac { x } { 7 } - \frac { x ^ { 5 } } { 5 } + \frac { c } { 4 x ^ { 4 } } = y$$

Solve for c

$$c=\frac{4x^{4}\left(7x^{5}-5x+35y\right)}{35}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 140x^{4}, the least common multiple of 7,5,4x^{4}.

$$20x^{4}x-28x^{4}x^{5}+35c=y\times 140x^{4}$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$20x^{5}-28x^{4}x^{5}+35c=y\times 140x^{4}$$

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

$$20x^{5}-28x^{9}+35c=y\times 140x^{4}$$

Subtract 20x^{5} from both sides.

$$-28x^{9}+35c=y\times 140x^{4}-20x^{5}$$

Add 28x^{9} to both sides.

$$35c=y\times 140x^{4}-20x^{5}+28x^{9}$$

The equation is in standard form.

$$35c=28x^{9}-20x^{5}+140yx^{4}$$

Divide both sides by 35.

$$\frac{35c}{35}=\frac{4x^{4}\left(7x^{5}-5x+35y\right)}{35}$$

Dividing by 35 undoes the multiplication by 35.

$$c=\frac{4x^{4}\left(7x^{5}-5x+35y\right)}{35}$$

Divide 4\left(35y-5x+7x^{5}\right)x^{4} by 35.

$$c=\frac{4x^{9}}{5}+4yx^{4}-\frac{4x^{5}}{7}$$