Solve x^2-6x=2x^2+6x

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

Solve for x

$$x=-12$$

$$x=0$$

Steps Using Factoring

Subtract 2x^{2} from both sides.

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

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

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

Subtract 6x from both sides.

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

Combine -6x and -6x to get -12x.

$$-x^{2}-12x=0$$

Factor out x.

$$x\left(-x-12\right)=0$$

To find equation solutions, solve x=0 and -x-12=0.

$$x=0 x=-12$$

Steps Using the Quadratic Formula

Subtract 2x^{2} from both sides.

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

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

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

Subtract 6x from both sides.

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

Combine -6x and -6x to get -12x.

$$-x^{2}-12x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, -12 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}}}{2\left(-1\right)}$$

Take the square root of \left(-12\right)^{2}.

$$x=\frac{-\left(-12\right)±12}{2\left(-1\right)}$$

The opposite of -12 is 12.

$$x=\frac{12±12}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{12±12}{-2}$$

Now solve the equation x=\frac{12±12}{-2} when ± is plus. Add 12 to 12.

$$x=\frac{24}{-2}$$

Divide 24 by -2.

$$x=-12$$

Now solve the equation x=\frac{12±12}{-2} when ± is minus. Subtract 12 from 12.

$$x=\frac{0}{-2}$$

Divide 0 by -2.

$$x=0$$

The equation is now solved.

$$x=-12 x=0$$

Steps for Completing the Square

Subtract 2x^{2} from both sides.

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

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

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

Subtract 6x from both sides.

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

Combine -6x and -6x to get -12x.

$$-x^{2}-12x=0$$

Divide both sides by -1.

$$\frac{-x^{2}-12x}{-1}=\frac{0}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x^{2}+\left(-\frac{12}{-1}\right)x=\frac{0}{-1}$$

Divide -12 by -1.

$$x^{2}+12x=\frac{0}{-1}$$

Divide 0 by -1.

$$x^{2}+12x=0$$

Divide 12, the coefficient of the x term, by 2 to get 6. Then add the square of 6 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+12x+6^{2}=6^{2}$$

Square 6.

$$x^{2}+12x+36=36$$

Factor x^{2}+12x+36. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+6\right)^{2}=36$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+6\right)^{2}}=\sqrt{36}$$

Simplify.

$$x+6=6 x+6=-6$$

Subtract 6 from both sides of the equation.

$$x=0 x=-12$$