4t^2+80t+12=-132

Solution for 4t^2+80t+12=-132 equation:

Simplifying
4t2 + 80t + 12 = -132

Reorder the terms:
12 + 80t + 4t2 = -132

Solving
12 + 80t + 4t2 = -132

Solving for variable 't'.

Reorder the terms:
12 + 132 + 80t + 4t2 = -132 + 132

Combine like terms: 12 + 132 = 144
144 + 80t + 4t2 = -132 + 132

Combine like terms: -132 + 132 = 0
144 + 80t + 4t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(36 + 20t + t2) = 0

Factor a trinomial.
4((18 + t)(2 + t)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(18 + t)' equal to zero and attempt to solve:

Simplifying
18 + t = 0

Solving
18 + t = 0

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

Add '-18' to each side of the equation.
18 + -18 + t = 0 + -18

Combine like terms: 18 + -18 = 0
0 + t = 0 + -18
t = 0 + -18

Combine like terms: 0 + -18 = -18
t = -18

Simplifying
t = -18
Subproblem 2
Set the factor '(2 + t)' equal to zero and attempt to solve:

Simplifying
2 + t = 0

Solving
2 + t = 0

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

Add '-2' to each side of the equation.
2 + -2 + t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + t = 0 + -2
t = 0 + -2

Combine like terms: 0 + -2 = -2
t = -2

Simplifying
t = -2
Solution
t = {-18, -2}