60t^2+120t-120=0

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

Simplifying
60t2 + 120t + -120 = 0

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

Solving
-120 + 120t + 60t2 = 0

Solving for variable 't'.

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

Ignore the factor 60.
Subproblem 1
Set the factor '(-2 + 2t + t2)' equal to zero and attempt to solve:

Simplifying
-2 + 2t + t2 = 0

Solving
-2 + 2t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 2t + 2 + t2 = 0 + 2

Reorder the terms:
-2 + 2 + 2t + t2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 2t + t2 = 0 + 2
2t + t2 = 0 + 2

Combine like terms: 0 + 2 = 2
2t + t2 = 2

The t term is 2t.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2t + 1 + t2 = 2 + 1

Reorder the terms:
1 + 2t + t2 = 2 + 1

Combine like terms: 2 + 1 = 3
1 + 2t + t2 = 3

Factor a perfect square on the left side:
(t + 1)(t + 1) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(t + 1) equal to 1.732050808 and -1.732050808.

Subproblem 1
t + 1 = 1.732050808

Simplifying
t + 1 = 1.732050808

Reorder the terms:
1 + t = 1.732050808

Solving
1 + t = 1.732050808

Solving for variable 't'.

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 = 1.732050808 + -1

Combine like terms: 1 + -1 = 0
0 + t = 1.732050808 + -1
t = 1.732050808 + -1

Combine like terms: 1.732050808 + -1 = 0.732050808
t = 0.732050808

Simplifying
t = 0.732050808

Subproblem 2
t + 1 = -1.732050808

Simplifying
t + 1 = -1.732050808

Reorder the terms:
1 + t = -1.732050808

Solving
1 + t = -1.732050808

Solving for variable 't'.

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 = -1.732050808 + -1

Combine like terms: 1 + -1 = 0
0 + t = -1.732050808 + -1
t = -1.732050808 + -1

Combine like terms: -1.732050808 + -1 = -2.732050808
t = -2.732050808

Simplifying
t = -2.732050808

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.732050808, -2.732050808}
Solution
t = {0.732050808, -2.732050808}