Solve 5x(x+6)=0

$$5x(x+6)=0$$

Solve for x

$$x=-6$$

$$x=0$$

Steps Using Factoring

Use the distributive property to multiply 5x by x+6.

$$5x^{2}+30x=0$$

Factor out x.

$$x\left(5x+30\right)=0$$

To find equation solutions, solve x=0 and 5x+30=0.

$$x=0 x=-6$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 5x by x+6.

$$5x^{2}+30x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 30 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-30±\sqrt{30^{2}}}{2\times 5}$$

Take the square root of 30^{2}.

$$x=\frac{-30±30}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{-30±30}{10}$$

Now solve the equation x=\frac{-30±30}{10} when ± is plus. Add -30 to 30.

$$x=\frac{0}{10}$$

Divide 0 by 10.

$$x=0$$

Now solve the equation x=\frac{-30±30}{10} when ± is minus. Subtract 30 from -30.

$$x=-\frac{60}{10}$$

Divide -60 by 10.

$$x=-6$$

The equation is now solved.

$$x=0 x=-6$$

Steps for Completing the Square

Use the distributive property to multiply 5x by x+6.

$$5x^{2}+30x=0$$

Divide both sides by 5.

$$\frac{5x^{2}+30x}{5}=\frac{0}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$x^{2}+\frac{30}{5}x=\frac{0}{5}$$

Divide 30 by 5.

$$x^{2}+6x=\frac{0}{5}$$

Divide 0 by 5.

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

Divide 6, the coefficient of the x term, by 2 to get 3. Then add the square of 3 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

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

Square 3.

$$x^{2}+6x+9=9$$

Factor x^{2}+6x+9. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+3\right)^{2}=9$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+3\right)^{2}}=\sqrt{9}$$

Simplify.

$$x+3=3 x+3=-3$$

Subtract 3 from both sides of the equation.

$$x=0 x=-6$$