Solve 3x(x+7)=0

$$3 x ( x + 7 ) = 0$$

Solve for x

$$x=-7$$

$$x=0$$

Steps Using Factoring

Use the distributive property to multiply 3x by x+7.

$$3x^{2}+21x=0$$

Factor out x.

$$x\left(3x+21\right)=0$$

To find equation solutions, solve x=0 and 3x+21=0.

$$x=0 x=-7$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 3x by x+7.

$$3x^{2}+21x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 21 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-21±\sqrt{21^{2}}}{2\times 3}$$

Take the square root of 21^{2}.

$$x=\frac{-21±21}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{-21±21}{6}$$

Now solve the equation x=\frac{-21±21}{6} when ± is plus. Add -21 to 21.

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

Divide 0 by 6.

$$x=0$$

Now solve the equation x=\frac{-21±21}{6} when ± is minus. Subtract 21 from -21.

$$x=-\frac{42}{6}$$

Divide -42 by 6.

$$x=-7$$

The equation is now solved.

$$x=0 x=-7$$

Steps for Completing the Square

Use the distributive property to multiply 3x by x+7.

$$3x^{2}+21x=0$$

Divide both sides by 3.

$$\frac{3x^{2}+21x}{3}=\frac{0}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$x^{2}+\frac{21}{3}x=\frac{0}{3}$$

Divide 21 by 3.

$$x^{2}+7x=\frac{0}{3}$$

Divide 0 by 3.

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

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.

$$x=0 x=-7$$