Solve for x 5x^3+30x^2+45x=0

$5 x^{3} + 30 x^{2} + 45 x = 0$

Factor the left side of the equation.

Factor $5 x$ out of $5 x^{3} + 30 x^{2} + 45 x$ .

Factor $5 x$ out of $5 x^{3}$ .

$5 x (x^{2}) + 30 x^{2} + 45 x = 0$

Factor $5 x$ out of $30 x^{2}$ .

$5 x (x^{2}) + 5 x (6 x) + 45 x = 0$

Factor $5 x$ out of $45 x$ .

$5 x (x^{2}) + 5 x (6 x) + 5 x (9) = 0$

Factor $5 x$ out of $5 x (x^{2}) + 5 x (6 x)$ .

$5 x (x^{2} + 6 x) + 5 x (9) = 0$

Factor $5 x$ out of $5 x (x^{2} + 6 x) + 5 x (9)$ .

$5 x (x^{2} + 6 x + 9) = 0$

Factor using the perfect square rule.

Rewrite $9$ as $3^{2}$ .

$5 x (x^{2} + 6 x + 3^{2}) = 0$

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

$6 x = 2 \cdot x \cdot 3$

Rewrite the polynomial.

$5 x (x^{2} + 2 \cdot x \cdot 3 + 3^{2}) = 0$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = x$ and $b = 3$ .

$5 x {(x + 3)}^{2} = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

${(x + 3)}^{2} = 0$

Set $x$ equal to $0$ .

$x = 0$

Set ${(x + 3)}^{2}$ equal to $0$ and solve for $x$ .

Set ${(x + 3)}^{2}$ equal to $0$ .

${(x + 3)}^{2} = 0$

Solve ${(x + 3)}^{2} = 0$ for $x$ .

Set the $x + 3$ equal to $0$ .

$x + 3 = 0$

Subtract $3$ from both sides of the equation.

$x = - 3$

The final solution is all the values that make $5 x {(x + 3)}^{2} = 0$ true.

$x = 0, - 3$