Solve x^8+x^7+x^6+x^5-{x}^4+{x}^3-2{x}^2+5x-5=6y

$${ x }^{ 8 } + { x }^{ 7 } + { x }^{ 6 } + { x }^{ 5 } - { x }^{ 4 } + { x }^{ 3 } -2 { x }^{ 2 } +5x-5=6y$$

Solve for y

$$y=\frac{x^{8}+x^{7}+x^{6}+x^{5}-x^{4}+x^{3}-2x^{2}+5x-5}{6}$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$6y=x^{8}+x^{7}+x^{6}+x^{5}-x^{4}+x^{3}-2x^{2}+5x-5$$

Divide both sides by 6.

$$\frac{6y}{6}=\frac{x^{8}+x^{7}+x^{6}+x^{5}-x^{4}+x^{3}-2x^{2}+5x-5}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$y=\frac{x^{8}+x^{7}+x^{6}+x^{5}-x^{4}+x^{3}-2x^{2}+5x-5}{6}$$

Divide -5+x^{8}+x^{7}+x^{5}-x^{4}-2x^{2}+x^{6}+5x+x^{3} by 6.

$$y=\frac{x^{8}}{6}+\frac{x^{7}}{6}+\frac{x^{6}}{6}+\frac{x^{5}}{6}-\frac{x^{4}}{6}+\frac{x^{3}}{6}-\frac{x^{2}}{3}+\frac{5x}{6}-\frac{5}{6}$$