Solve 4x(x+7)=0

$$4x(x+7)=0$$

Solve for x

$$x=-7$$

$$x=0$$

Steps Using Factoring

Use the distributive property to multiply 4x by x+7.

$$4x^{2}+28x=0$$

Factor out x.

$$x\left(4x+28\right)=0$$

To find equation solutions, solve x=0 and 4x+28=0.

$$x=0 x=-7$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 4x by x+7.

$$4x^{2}+28x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 28 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-28±\sqrt{28^{2}}}{2\times 4}$$

Take the square root of 28^{2}.

$$x=\frac{-28±28}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{-28±28}{8}$$

Now solve the equation x=\frac{-28±28}{8} when ± is plus. Add -28 to 28.

$$x=\frac{0}{8}$$

Divide 0 by 8.

$$x=0$$

Now solve the equation x=\frac{-28±28}{8} when ± is minus. Subtract 28 from -28.

$$x=-\frac{56}{8}$$

Divide -56 by 8.

$$x=-7$$

The equation is now solved.

$$x=0 x=-7$$

Steps for Completing the Square

Use the distributive property to multiply 4x by x+7.

$$4x^{2}+28x=0$$

Divide both sides by 4.

$$\frac{4x^{2}+28x}{4}=\frac{0}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x^{2}+\frac{28}{4}x=\frac{0}{4}$$

Divide 28 by 4.

$$x^{2}+7x=\frac{0}{4}$$

Divide 0 by 4.

$$x^{2}+7x=0$$

Divide 7, the coefficient of the x term, by 2 to get \frac{7}{2}. Then add the square of \frac{7}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+7x+\left(\frac{7}{2}\right)^{2}=\left(\frac{7}{2}\right)^{2}$$

Square \frac{7}{2} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+7x+\frac{49}{4}=\frac{49}{4}$$

Factor x^{2}+7x+\frac{49}{4}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{7}{2}\right)^{2}=\frac{49}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{7}{2}\right)^{2}}=\sqrt{\frac{49}{4}}$$

Simplify.

$$x+\frac{7}{2}=\frac{7}{2} x+\frac{7}{2}=-\frac{7}{2}$$

Subtract \frac{7}{2} from both sides of the equation.

$$x=0 x=-7$$