Solve 0=xleft(5x+6right)

$$0 = x \left( 5x+6 \right)$$

Solve for x

$$x = -\frac{6}{5} = -1\frac{1}{5} = -1.2$$

$$x=0$$

Steps Using Factoring

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

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

Swap sides so that all variable terms are on the left hand side.

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

Factor out x.

$$x\left(5x+6\right)=0$$

To find equation solutions, solve x=0 and 5x+6=0.

$$x=0 x=-\frac{6}{5}$$

Steps Using the Quadratic Formula

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

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

Swap sides so that all variable terms are on the left hand side.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 6 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-6±\sqrt{6^{2}}}{2\times 5}$$

Take the square root of 6^{2}.

$$x=\frac{-6±6}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{-6±6}{10}$$

Now solve the equation x=\frac{-6±6}{10} when ± is plus. Add -6 to 6.

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

Divide 0 by 10.

$$x=0$$

Now solve the equation x=\frac{-6±6}{10} when ± is minus. Subtract 6 from -6.

$$x=-\frac{12}{10}$$

Reduce the fraction \frac{-12}{10} to lowest terms by extracting and canceling out 2.

$$x=-\frac{6}{5}$$

The equation is now solved.

$$x=0 x=-\frac{6}{5}$$

Steps for Completing the Square

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

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

Swap sides so that all variable terms are on the left hand side.

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

Divide both sides by 5.

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

Dividing by 5 undoes the multiplication by 5.

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

Divide 0 by 5.

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

Divide \frac{6}{5}, the coefficient of the x term, by 2 to get \frac{3}{5}. Then add the square of \frac{3}{5} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{6}{5}x+\left(\frac{3}{5}\right)^{2}=\left(\frac{3}{5}\right)^{2}$$

Square \frac{3}{5} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{6}{5}x+\frac{9}{25}=\frac{9}{25}$$

Factor x^{2}+\frac{6}{5}x+\frac{9}{25}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{3}{5}\right)^{2}=\frac{9}{25}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{3}{5}\right)^{2}}=\sqrt{\frac{9}{25}}$$

Simplify.

$$x+\frac{3}{5}=\frac{3}{5} x+\frac{3}{5}=-\frac{3}{5}$$

Subtract \frac{3}{5} from both sides of the equation.

$$x=0 x=-\frac{6}{5}$$