60t^2+120t+60=0

Solution for 60t^2+120t+60=0 equation:

Simplifying
60t2 + 120t + 60 = 0

Reorder the terms:
60 + 120t + 60t2 = 0

Solving
60 + 120t + 60t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '60'.
60(1 + 2t + t2) = 0

Factor a trinomial.
60((1 + t)(1 + t)) = 0

Ignore the factor 60.
Subproblem 1
Set the factor '(1 + t)' equal to zero and attempt to solve:

Simplifying
1 + t = 0

Solving
1 + t = 0

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

Add '-1' to each side of the equation.
1 + -1 + t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + t = 0 + -1
t = 0 + -1

Combine like terms: 0 + -1 = -1
t = -1

Simplifying
t = -1
Subproblem 2
Set the factor '(1 + t)' equal to zero and attempt to solve:

Simplifying
1 + t = 0

Solving
1 + t = 0

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

Add '-1' to each side of the equation.
1 + -1 + t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + t = 0 + -1
t = 0 + -1

Combine like terms: 0 + -1 = -1
t = -1

Simplifying
t = -1
Solution
t = {-1, -1}