Solve (x+4)(x-11)=x^2*Z

$$( x + 4 ) ( x - 11 ) = x ^ { 2 } \cdot Z$$

Solve for Z

$$Z=\frac{\left(x-11\right)\left(x+4\right)}{x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply x+4 by x-11 and combine like terms.

$$x^{2}-7x-44=x^{2}Z$$

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

$$x^{2}Z=x^{2}-7x-44$$

Divide both sides by x^{2}.

$$\frac{x^{2}Z}{x^{2}}=\frac{\left(x-11\right)\left(x+4\right)}{x^{2}}$$

Dividing by x^{2} undoes the multiplication by x^{2}.

$$Z=\frac{\left(x-11\right)\left(x+4\right)}{x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{225-176Z}+7}{2\left(1-Z\right)}\text{; }x=\frac{-\sqrt{225-176Z}+7}{2\left(1-Z\right)}\text{, }&Z\neq 1\\x=-\frac{44}{7}\text{, }&Z=1\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{225-176Z}+7}{2\left(1-Z\right)}\text{; }x=\frac{-\sqrt{225-176Z}+7}{2\left(1-Z\right)}\text{, }&Z\neq 1\text{ and }Z\leq \frac{225}{176}\\x=-\frac{44}{7}\text{, }&Z=1\end{matrix}\right.$$