Solve 2(2x-3)+2x^2=x(x+4)-6

$$2 ( 2 x - 3 ) + 2 x ^ { 2 } = x ( x + 4 ) - 6$$

Solve for x

$$x=0$$

Steps by Finding Square Root

Use the distributive property to multiply 2 by 2x-3.

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

Use the distributive property to multiply x by x+4.

$$4x-6+2x^{2}=x^{2}+4x-6$$

Subtract x^{2} from both sides.

$$4x-6+2x^{2}-x^{2}=4x-6$$

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

$$4x-6+x^{2}=4x-6$$

Subtract 4x from both sides.

$$4x-6+x^{2}-4x=-6$$

Combine 4x and -4x to get 0.

$$-6+x^{2}=-6$$

Add 6 to both sides.

$$x^{2}=-6+6$$

Add -6 and 6 to get 0.

$$x^{2}=0$$

Take the square root of both sides of the equation.

$$x=0 x=0$$

The equation is now solved. Solutions are the same.

$$x=0$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 2 by 2x-3.

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

Use the distributive property to multiply x by x+4.

$$4x-6+2x^{2}=x^{2}+4x-6$$

Subtract x^{2} from both sides.

$$4x-6+2x^{2}-x^{2}=4x-6$$

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

$$4x-6+x^{2}=4x-6$$

Subtract 4x from both sides.

$$4x-6+x^{2}-4x=-6$$

Combine 4x and -4x to get 0.

$$-6+x^{2}=-6$$

Add 6 to both sides.

$$-6+x^{2}+6=0$$

Add -6 and 6 to get 0.

$$x^{2}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}}}{2}$$

Take the square root of 0^{2}.

$$x=\frac{0±0}{2}$$

Divide 0 by 2.

$$x=0$$