Solve 3x^2=6x

$$3 x ^ { 2 } = 6 x$$

Solve for x

$$x=2$$

$$x=0$$

Steps Using Factoring

Subtract 6x from both sides.

$$3x^{2}-6x=0$$

Factor out x.

$$x\left(3x-6\right)=0$$

To find equation solutions, solve x=0 and 3x-6=0.

$$x=0 x=2$$

Steps Using the Quadratic Formula

Subtract 6x from both sides.

$$3x^{2}-6x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, -6 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}}}{2\times 3}$$

Take the square root of \left(-6\right)^{2}.

$$x=\frac{-\left(-6\right)±6}{2\times 3}$$

The opposite of -6 is 6.

$$x=\frac{6±6}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{6±6}{6}$$

Now solve the equation x=\frac{6±6}{6} when ± is plus. Add 6 to 6.

$$x=\frac{12}{6}$$

Divide 12 by 6.

$$x=2$$

Now solve the equation x=\frac{6±6}{6} when ± is minus. Subtract 6 from 6.

$$x=\frac{0}{6}$$

Divide 0 by 6.

$$x=0$$

The equation is now solved.

$$x=2 x=0$$

Steps for Completing the Square

Subtract 6x from both sides.

$$3x^{2}-6x=0$$

Divide both sides by 3.

$$\frac{3x^{2}-6x}{3}=\frac{0}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$x^{2}+\left(-\frac{6}{3}\right)x=\frac{0}{3}$$

Divide -6 by 3.

$$x^{2}-2x=\frac{0}{3}$$

Divide 0 by 3.

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

Divide -2, the coefficient of the x term, by 2 to get -1. Then add the square of -1 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

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

Factor x^{2}-2x+1. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

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

Take the square root of both sides of the equation.

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

Simplify.

$$x-1=1 x-1=-1$$

Add 1 to both sides of the equation.

$$x=2 x=0$$