3y^2+21y=-36

Solution for 3y^2+21y=-36 equation:

Simplifying
3y2 + 21y = -36

Reorder the terms:
21y + 3y2 = -36

Solving
21y + 3y2 = -36

Solving for variable 'y'.

Reorder the terms:
36 + 21y + 3y2 = -36 + 36

Combine like terms: -36 + 36 = 0
36 + 21y + 3y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(12 + 7y + y2) = 0

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

Ignore the factor 3.
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}