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

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

Solve for x

$$x=-\frac{3}{4}=-0.75$$

Steps for Solving Linear Equation

Use the distributive property to multiply -3 by x+1.

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

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

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

Subtract \left(-x\right)x from both sides.

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

Add x to both sides.

$$x^{2}-3x-3-2x\left(x+1\right)-\left(-x\right)x+x=0$$

Multiply -1 and 2 to get -2.

$$x^{2}-3x-3-2x\left(x+1\right)-\left(-xx\right)+x=0$$

Use the distributive property to multiply -2x by x+1.

$$x^{2}-3x-3-2x^{2}-2x-\left(-xx\right)+x=0$$

Combine x^{2} and -2x^{2} to get -x^{2}.

$$-x^{2}-3x-3-2x-\left(-xx\right)+x=0$$

Combine -3x and -2x to get -5x.

$$-x^{2}-5x-3-\left(-xx\right)+x=0$$

Multiply x and x to get x^{2}.

$$-x^{2}-5x-3-\left(-x^{2}\right)+x=0$$

Multiply -1 and -1 to get 1.

$$-x^{2}-5x-3+x^{2}+x=0$$

Combine -x^{2} and x^{2} to get 0.

$$-5x-3+x=0$$

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

$$-4x-3=0$$

Add 3 to both sides. Anything plus zero gives itself.

$$-4x=3$$

Divide both sides by -4.

$$x=\frac{3}{-4}$$

Fraction \frac{3}{-4} can be rewritten as -\frac{3}{4} by extracting the negative sign.

$$x=-\frac{3}{4}$$