12t^2+48t+48=0

Solution for 12t^2+48t+48=0 equation:

Simplifying
12t2 + 48t + 48 = 0

Reorder the terms:
48 + 48t + 12t2 = 0

Solving
48 + 48t + 12t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '12'.
12(4 + 4t + t2) = 0

Factor a trinomial.
12((2 + t)(2 + t)) = 0

Ignore the factor 12.
Subproblem 1
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
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 = {-2, -2}