Solve 3x^2+15x+3x=0

$$3 { x }^{ 2 } +15x+3x=0$$

Solve for x

$$x=-6$$

$$x=0$$

Steps Using Factoring

Factor out x.

$$x\left(3x+15+3\right)=0$$

To find equation solutions, solve x=0 and 3x+18=0.

$$x=0 x=-6$$

Steps Using the Quadratic Formula

Combine 15x and 3x to get 18x.

$$3x^{2}+18x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 18 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-18±\sqrt{18^{2}}}{2\times 3}$$

Take the square root of 18^{2}.

$$x=\frac{-18±18}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{-18±18}{6}$$

Now solve the equation x=\frac{-18±18}{6} when ± is plus. Add -18 to 18.

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

Divide 0 by 6.

$$x=0$$

Now solve the equation x=\frac{-18±18}{6} when ± is minus. Subtract 18 from -18.

$$x=-\frac{36}{6}$$

Divide -36 by 6.

$$x=-6$$

The equation is now solved.

$$x=0 x=-6$$

Steps for Completing the Square

Combine 15x and 3x to get 18x.

$$3x^{2}+18x=0$$

Divide both sides by 3.

$$\frac{3x^{2}+18x}{3}=\frac{0}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$x^{2}+\frac{18}{3}x=\frac{0}{3}$$

Divide 18 by 3.

$$x^{2}+6x=\frac{0}{3}$$

Divide 0 by 3.

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

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.

$$x=0 x=-6$$