Solve 7x=left(x5right)^2*9x

$$7x= { \left(x5 \right) }^{ 2 } \times 9x$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&x_{5}=-\frac{\sqrt{7}}{3}\text{ or }x_{5}=\frac{\sqrt{7}}{3}\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract x_{5}^{2}\times 9x from both sides.

$$7x-x_{5}^{2}\times 9x=0$$

Multiply -1 and 9 to get -9.

$$7x-9x_{5}^{2}x=0$$

Combine all terms containing x.

$$\left(7-9x_{5}^{2}\right)x=0$$

Divide 0 by 7-9x_{5}^{2}.

$$x=0$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&|x_{5}|=\frac{\sqrt{7}}{3}\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract x_{5}^{2}\times 9x from both sides.

$$7x-x_{5}^{2}\times 9x=0$$

Multiply -1 and 9 to get -9.

$$7x-9x_{5}^{2}x=0$$

Combine all terms containing x.

$$\left(7-9x_{5}^{2}\right)x=0$$

Divide 0 by 7-9x_{5}^{2}.

$$x=0$$

Solve for x_5 (complex solution)

$$\left\{\begin{matrix}\\x_{5}=-\frac{\sqrt{7}}{3}\text{; }x_{5}=\frac{\sqrt{7}}{3}\text{, }&\text{unconditionally}\\x_{5}\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Solve for x_5

$$\left\{\begin{matrix}\\x_{5}=\frac{\sqrt{7}}{3}\text{; }x_{5}=-\frac{\sqrt{7}}{3}\text{, }&\text{unconditionally}\\x_{5}\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$