Solve (x-1)(x^2+x-1)-2x=x(x-1)(x+1)+2x-3

$$( x - 1 ) ( x ^ { 2 } + x - 1 ) - 2 x = x ( x - 1 ) ( x + 1 ) + 2 x - 3$$

Solve for x

$$x=\frac{4}{5}=0.8$$

Steps for Solving Linear Equation

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

$$x^{3}-2x+1-2x=x\left(x-1\right)\left(x+1\right)+2x-3$$

Combine -2x and -2x to get -4x.

$$x^{3}-4x+1=x\left(x-1\right)\left(x+1\right)+2x-3$$

Use the distributive property to multiply x by x-1.

$$x^{3}-4x+1=\left(x^{2}-x\right)\left(x+1\right)+2x-3$$

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

$$x^{3}-4x+1=x^{3}-x+2x-3$$

Combine -x and 2x to get x.

$$x^{3}-4x+1=x^{3}+x-3$$

Subtract x^{3} from both sides.

$$x^{3}-4x+1-x^{3}=x-3$$

Combine x^{3} and -x^{3} to get 0.

$$-4x+1=x-3$$

Subtract x from both sides.

$$-4x+1-x=-3$$

Combine -4x and -x to get -5x.

$$-5x+1=-3$$

Subtract 1 from both sides.

$$-5x=-3-1$$

Subtract 1 from -3 to get -4.

$$-5x=-4$$

Divide both sides by -5.

$$x=\frac{-4}{-5}$$

Fraction \frac{-4}{-5} can be simplified to \frac{4}{5} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{4}{5}$$