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5x^{2}+30x=0
Add 30x to both sides.
x\left(5x+30\right)=0
Factor out x.
x=0 x=-6
To find equation solutions, solve x=0 and 5x+30=0.
5x^{2}+30x=0
Add 30x to both sides.
x=\frac{-30±\sqrt{30^{2}}}{2\times 5}
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±30}{2\times 5}
Take the square root of 30^{2}.
x=\frac{-30±30}{10}
Multiply 2 times 5.
x=\frac{0}{10}
Now solve the equation x=\frac{-30±30}{10} when ± is plus. Add -30 to 30.
x=0
Divide 0 by 10.
x=-\frac{60}{10}
Now solve the equation x=\frac{-30±30}{10} when ± is minus. Subtract 30 from -30.
x=-6
Divide -60 by 10.
x=0 x=-6
The equation is now solved.
5x^{2}+30x=0
Add 30x to both sides.
\frac{5x^{2}+30x}{5}=\frac{0}{5}
Divide both sides by 5.
x^{2}+\frac{30}{5}x=\frac{0}{5}
Dividing by 5 undoes the multiplication by 5.
x^{2}+6x=\frac{0}{5}
Divide 30 by 5.
x^{2}+6x=0
Divide 0 by 5.
x^{2}+6x+3^{2}=3^{2}
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+9=9
Square 3.
\left(x+3\right)^{2}=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}.
\sqrt{\left(x+3\right)^{2}}=\sqrt{9}
Take the square root of both sides of the equation.
x+3=3 x+3=-3
Simplify.
x=0 x=-6
Subtract 3 from both sides of the equation.