Solve for y y(y+4)=-4

$y (y + 4) = - 4$

Step 1

Simplify $y (y + 4)$ .

Apply the distributive property.

$y \cdot y + y \cdot 4 = - 4$

Simplify the expression.

Multiply $y$ by $y$ .

$y^{2} + y \cdot 4 = - 4$

Move $4$ to the left of $y$ .

$y^{2} + 4 y = - 4$

Step 2

Add $4$ to both sides of the equation.

$y^{2} + 4 y + 4 = 0$

Step 3

Factor using the perfect square rule.

Rewrite $4$ as $2^{2}$ .

$y^{2} + 4 y + 2^{2} = 0$

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

$4 y = 2 \cdot y \cdot 2$

Rewrite the polynomial.

$y^{2} + 2 \cdot y \cdot 2 + 2^{2} = 0$

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

${(y + 2)}^{2} = 0$

Step 4

Set the $y + 2$ equal to $0$ .

$y + 2 = 0$

Step 5

Subtract $2$ from both sides of the equation.

$y = - 2$