-4y^2-48y-108=0

Solution for -4y^2-48y-108=0 equation:

Simplifying
-4y2 + -48y + -108 = 0

Reorder the terms:
-108 + -48y + -4y2 = 0

Solving
-108 + -48y + -4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '-4'.
-4(27 + 12y + y2) = 0

Factor a trinomial.
-4((9 + y)(3 + y)) = 0

Ignore the factor -4.
Subproblem 1
Set the factor '(9 + y)' equal to zero and attempt to solve:

Simplifying
9 + y = 0

Solving
9 + y = 0

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

Add '-9' to each side of the equation.
9 + -9 + y = 0 + -9

Combine like terms: 9 + -9 = 0
0 + y = 0 + -9
y = 0 + -9

Combine like terms: 0 + -9 = -9
y = -9

Simplifying
y = -9
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 = {-9, -3}