y(y+7)=-12

Solution for y(y+7)=-12 equation:

Simplifying
y(y + 7) = -12

Reorder the terms:
y(7 + y) = -12
(7 * y + y * y) = -12
(7y + y2) = -12

Solving
7y + y2 = -12

Solving for variable 'y'.

Reorder the terms:
12 + 7y + y2 = -12 + 12

Combine like terms: -12 + 12 = 0
12 + 7y + y2 = 0

Factor a trinomial.
(4 + y)(3 + y) = 0

Subproblem 1
Set the factor '(4 + y)' equal to zero and attempt to solve:

Simplifying
4 + y = 0

Solving
4 + y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + y = 0 + -4
y = 0 + -4

Combine like terms: 0 + -4 = -4
y = -4

Simplifying
y = -4
Subproblem 2
Set the factor '(3 + y)' equal to zero and attempt to solve:

Simplifying
3 + y = 0

Solving
3 + y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + y = 0 + -3
y = 0 + -3

Combine like terms: 0 + -3 = -3
y = -3

Simplifying
y = -3
Solution
y = {-4, -3}