3y^2+13y=-12

Solution for 3y^2+13y=-12 equation:

Simplifying
3y2 + 13y = -12

Reorder the terms:
13y + 3y2 = -12

Solving
13y + 3y2 = -12

Solving for variable 'y'.

Reorder the terms:
12 + 13y + 3y2 = -12 + 12

Combine like terms: -12 + 12 = 0
12 + 13y + 3y2 = 0

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

Subproblem 1
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
Subproblem 2
Set the factor '(4 + 3y)' equal to zero and attempt to solve:

Simplifying
4 + 3y = 0

Solving
4 + 3y = 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 + 3y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3y = 0 + -4
3y = 0 + -4

Combine like terms: 0 + -4 = -4
3y = -4

Divide each side by '3'.
y = -1.333333333

Simplifying
y = -1.333333333
Solution
y = {-3, -1.333333333}