Solve 6x^2-4x8x(x^2-1)=0

$$6 x ^ { 2 } - 4 x 8 x ( x ^ { 2 } - 1 ) = 0$$

Solve for x_8

$$\left\{\begin{matrix}x_{8}=-\frac{3x}{2\left(1-x^{2}\right)}\text{, }&|x|\neq 1\\x_{8}\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply -1 and 4 to get -4.

$$6x^{2}-4x_{8}x\left(x^{2}-1\right)=0$$

Use the distributive property to multiply -4x_{8}x by x^{2}-1.

$$6x^{2}-4x_{8}x^{3}+4xx_{8}=0$$

Subtract 6x^{2} from both sides. Anything subtracted from zero gives its negation.

$$-4x_{8}x^{3}+4xx_{8}=-6x^{2}$$

Combine all terms containing x_{8}.

$$\left(-4x^{3}+4x\right)x_{8}=-6x^{2}$$

The equation is in standard form.

$$\left(4x-4x^{3}\right)x_{8}=-6x^{2}$$

Divide both sides by -4x^{3}+4x.

$$\frac{\left(4x-4x^{3}\right)x_{8}}{4x-4x^{3}}=-\frac{6x^{2}}{4x-4x^{3}}$$

Dividing by -4x^{3}+4x undoes the multiplication by -4x^{3}+4x.

$$x_{8}=-\frac{6x^{2}}{4x-4x^{3}}$$

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

$$x_{8}=-\frac{3x}{2\left(1-x^{2}\right)}$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=-\frac{\sqrt{16x_{8}^{2}+9}-3}{4x_{8}}\text{; }x=\frac{\sqrt{16x_{8}^{2}+9}+3}{4x_{8}}\text{, }&x_{8}\neq 0\end{matrix}\right.$$