Use the distributive property to multiply $2x$ by $x-3$.
$$2x^{2}-6x=0$$
Factor out $x$.
$$x\left(2x-6\right)=0$$
To find equation solutions, solve $x=0$ and $2x-6=0$.
$$x=0$$ $$x=3$$
Steps Using the Quadratic Formula
Use the distributive property to multiply $2x$ by $x-3$.
$$2x^{2}-6x=0$$
This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $2$ for $a$, $-6$ for $b$, and $0$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.
Now solve the equation $x=\frac{6±6}{4}$ when $±$ is plus. Add $6$ to $6$.
$$x=\frac{12}{4}$$
Divide $12$ by $4$.
$$x=3$$
Now solve the equation $x=\frac{6±6}{4}$ when $±$ is minus. Subtract $6$ from $6$.
$$x=\frac{0}{4}$$
Divide $0$ by $4$.
$$x=0$$
The equation is now solved.
$$x=3$$ $$x=0$$
Steps for Completing the Square
Use the distributive property to multiply $2x$ by $x-3$.
$$2x^{2}-6x=0$$
Divide both sides by $2$.
$$\frac{2x^{2}-6x}{2}=\frac{0}{2}$$
Dividing by $2$ undoes the multiplication by $2$.
$$x^{2}+\left(-\frac{6}{2}\right)x=\frac{0}{2}$$
Divide $-6$ by $2$.
$$x^{2}-3x=\frac{0}{2}$$
Divide $0$ by $2$.
$$x^{2}-3x=0$$
Divide $-3$, the coefficient of the $x$ term, by $2$ to get $-\frac{3}{2}$. Then add the square of $-\frac{3}{2}$ to both sides of the equation. This step makes the left hand side of the equation a perfect square.
