Solve 6x^2-6x=2(1-2x)-2-x(2-x)

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

Solve for x

$$x=0$$

Steps by Finding Square Root

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

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

Subtract 2 from 2 to get 0.

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

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

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

To find the opposite of 2x-x^{2}, find the opposite of each term.

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

Combine -4x and -2x to get -6x.

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

Add 6x to both sides.

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

Combine -6x and 6x to get 0.

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

Subtract x^{2} from both sides.

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

Combine 6x^{2} and -x^{2} to get 5x^{2}.

$$5x^{2}=0$$

Divide both sides by 5. Zero divided by any non-zero number gives zero.

$$x^{2}=0$$

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 1-2x.

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

Subtract 2 from 2 to get 0.

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

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

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

To find the opposite of 2x-x^{2}, find the opposite of each term.

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

Combine -4x and -2x to get -6x.

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

Add 6x to both sides.

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

Combine -6x and 6x to get 0.

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

Subtract x^{2} from both sides.

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

Combine 6x^{2} and -x^{2} to get 5x^{2}.

$$5x^{2}=0$$

Divide both sides by 5. Zero divided by any non-zero number gives zero.

$$x^{2}=0$$

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.

$$x=0$$