Solve for x (x^3+10x^2+25x)/(x+5)=0

$\frac{x^{3} + 10 x^{2} + 25 x}{x + 5} = 0$

Set the numerator equal to zero.

$x^{3} + 10 x^{2} + 25 x = 0$

Solve the equation for $x$ .

Factor the left side of the equation.

Factor $x$ out of $x^{3} + 10 x^{2} + 25 x$ .

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

$x \cdot x^{2} + 10 x^{2} + 25 x = 0$

Factor $x$ out of $10 x^{2}$ .

$x \cdot x^{2} + x (10 x) + 25 x = 0$

Factor $x$ out of $25 x$ .

$x \cdot x^{2} + x (10 x) + x \cdot 25 = 0$

Factor $x$ out of $x \cdot x^{2} + x (10 x)$ .

$x (x^{2} + 10 x) + x \cdot 25 = 0$

Factor $x$ out of $x (x^{2} + 10 x) + x \cdot 25$ .

$x (x^{2} + 10 x + 25) = 0$

Factor using the perfect square rule.

Rewrite $25$ as $5^{2}$ .

$x (x^{2} + 10 x + 5^{2}) = 0$

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

$10 x = 2 \cdot x \cdot 5$

Rewrite the polynomial.

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

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = x$ and $b = 5$ .

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

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

$x = 0$

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

Set $x$ equal to $0$ .

$x = 0$

Set ${(x + 5)}^{2}$ equal to $0$ and solve for $x$ .

Set ${(x + 5)}^{2}$ equal to $0$ .

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

Solve ${(x + 5)}^{2} = 0$ for $x$ .

Set the $x + 5$ equal to $0$ .

$x + 5 = 0$

Subtract $5$ from both sides of the equation.

$x = - 5$

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

$x = 0, - 5$

Exclude the solutions that do not make $\frac{x^{3} + 10 x^{2} + 25 x}{x + 5} = 0$ true.

$x = 0$