Solve for u 5u(u+2)+5=0

$5 u (u + 2) + 5 = 0$

Simplify each term.

Apply the distributive property.

$5 u \cdot u + 5 u \cdot 2 + 5 = 0$

Multiply $u$ by $u$ by adding the exponents.

Move $u$ .

$5 (u \cdot u) + 5 u \cdot 2 + 5 = 0$

Multiply $u$ by $u$ .

$5 u^{2} + 5 u \cdot 2 + 5 = 0$

Multiply $2$ by $5$ .

$5 u^{2} + 10 u + 5 = 0$

Factor the left side of the equation.

Factor $5$ out of $5 u^{2} + 10 u + 5$ .

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

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

Factor $5$ out of $10 u$ .

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

Factor $5$ out of $5$ .

$5 (u^{2}) + 5 (2 u) + 5 (1) = 0$

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

$5 (u^{2} + 2 u) + 5 (1) = 0$

Factor $5$ out of $5 (u^{2} + 2 u) + 5 (1)$ .

$5 (u^{2} + 2 u + 1) = 0$

Factor using the perfect square rule.

Rewrite $1$ as $1^{2}$ .

$5 (u^{2} + 2 u + 1^{2}) = 0$

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

$2 u = 2 \cdot u \cdot 1$

Rewrite the polynomial.

$5 (u^{2} + 2 \cdot u \cdot 1 + 1^{2}) = 0$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = u$ and $b = 1$ .

$5 {(u + 1)}^{2} = 0$

Divide each term in $5 {(u + 1)}^{2} = 0$ by $5$ and simplify.

Divide each term in $5 {(u + 1)}^{2} = 0$ by $5$ .

$\frac{5 {(u + 1)}^{2}}{5} = \frac{0}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 {(u + 1)}^{2}}{5} = \frac{0}{5}$

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

${(u + 1)}^{2} = \frac{0}{5}$

Simplify the right side.

Divide $0$ by $5$ .

${(u + 1)}^{2} = 0$

Set the $u + 1$ equal to $0$ .

$u + 1 = 0$

Subtract $1$ from both sides of the equation.

$u = - 1$

Solve for u 5u(u+2)+5=0

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