y(y+12)=-35

Solution for y(y+12)=-35 equation:

Simplifying
y(y + 12) = -35

Reorder the terms:
y(12 + y) = -35
(12 * y + y * y) = -35
(12y + y2) = -35

Solving
12y + y2 = -35

Solving for variable 'y'.

Reorder the terms:
35 + 12y + y2 = -35 + 35

Combine like terms: -35 + 35 = 0
35 + 12y + y2 = 0

Factor a trinomial.
(7 + y)(5 + y) = 0

Subproblem 1
Set the factor '(7 + y)' equal to zero and attempt to solve:

Simplifying
7 + y = 0

Solving
7 + y = 0

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

Add '-7' to each side of the equation.
7 + -7 + y = 0 + -7

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

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

Simplifying
y = -7
Subproblem 2
Set the factor '(5 + y)' equal to zero and attempt to solve:

Simplifying
5 + y = 0

Solving
5 + y = 0

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

Add '-5' to each side of the equation.
5 + -5 + y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + y = 0 + -5
y = 0 + -5

Combine like terms: 0 + -5 = -5
y = -5

Simplifying
y = -5
Solution
y = {-7, -5}