Solve y=(3X+7)(X-1)^2V

$$y = ( 3 X + 7 ) ( X - 1 ) ^ { 2 } V$$

Solve for V

$$\left\{\begin{matrix}V=\frac{y}{\left(3X+7\right)\left(X-1\right)^{2}}\text{, }&X\neq 1\text{ and }X\neq -\frac{7}{3}\\V\in \mathrm{R}\text{, }&\left(X=-\frac{7}{3}\text{ or }X=1\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(X-1\right)^{2}.

$$y=\left(3X+7\right)\left(X^{2}-2X+1\right)V$$

Use the distributive property to multiply 3X+7 by X^{2}-2X+1 and combine like terms.

$$y=\left(3X^{3}+X^{2}-11X+7\right)V$$

Use the distributive property to multiply 3X^{3}+X^{2}-11X+7 by V.

$$y=3X^{3}V+X^{2}V-11XV+7V$$

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

$$3X^{3}V+X^{2}V-11XV+7V=y$$

Combine all terms containing V.

$$\left(3X^{3}+X^{2}-11X+7\right)V=y$$

Divide both sides by 3X^{3}+X^{2}-11X+7.

$$\frac{\left(3X^{3}+X^{2}-11X+7\right)V}{3X^{3}+X^{2}-11X+7}=\frac{y}{3X^{3}+X^{2}-11X+7}$$

Dividing by 3X^{3}+X^{2}-11X+7 undoes the multiplication by 3X^{3}+X^{2}-11X+7.

$$V=\frac{y}{3X^{3}+X^{2}-11X+7}$$

Divide y by 3X^{3}+X^{2}-11X+7.

$$V=\frac{y}{\left(3X+7\right)\left(X-1\right)^{2}}$$