Solve by Factoring 5x^2+60x+180=0

$5 x^{2} + 60 x + 180 = 0$

Step 1

Factor $5$ out of $5 x^{2} + 60 x + 180$ .

Factor $5$ out of $5 x^{2}$ .

$5 (x^{2}) + 60 x + 180 = 0$

Factor $5$ out of $60 x$ .

$5 (x^{2}) + 5 (12 x) + 180 = 0$

Factor $5$ out of $180$ .

$5 x^{2} + 5 (12 x) + 5 \cdot 36 = 0$

Factor $5$ out of $5 x^{2} + 5 (12 x)$ .

$5 (x^{2} + 12 x) + 5 \cdot 36 = 0$

Factor $5$ out of $5 (x^{2} + 12 x) + 5 \cdot 36$ .

$5 (x^{2} + 12 x + 36) = 0$

Step 2

Factor using the perfect square rule.

Rewrite $36$ as $6^{2}$ .

$5 (x^{2} + 12 x + 6^{2}) = 0$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$12 x = 2 \cdot x \cdot 6$

Rewrite the polynomial.

$5 (x^{2} + 2 \cdot x \cdot 6 + 6^{2}) = 0$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = x$ and $b = 6$ .

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

Step 3

Divide each term in $5 {(x + 6)}^{2} = 0$ by $5$ and simplify.

Divide each term in $5 {(x + 6)}^{2} = 0$ by $5$ .

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

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Divide ${(x + 6)}^{2}$ by $1$ .

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

Simplify the right side.

Divide $0$ by $5$ .

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

Step 4

Set the $x + 6$ equal to $0$ .

$x + 6 = 0$

Step 5

Subtract $6$ from both sides of the equation.

$x = - 6$