60t^2+120t-50=0

Solution for 60t^2+120t-50=0 equation:

Simplifying
60t2 + 120t + -50 = 0

Reorder the terms:
-50 + 120t + 60t2 = 0

Solving
-50 + 120t + 60t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-5 + 12t + 6t2) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(-5 + 12t + 6t2)' equal to zero and attempt to solve:

Simplifying
-5 + 12t + 6t2 = 0

Solving
-5 + 12t + 6t2 = 0

Begin completing the square.  Divide all terms by
6 the coefficient of the squared term: 

Divide each side by '6'.
-0.8333333333 + 2t + t2 = 0

Move the constant term to the right:

Add '0.8333333333' to each side of the equation.
-0.8333333333 + 2t + 0.8333333333 + t2 = 0 + 0.8333333333

Reorder the terms:
-0.8333333333 + 0.8333333333 + 2t + t2 = 0 + 0.8333333333

Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000
0.0000000000 + 2t + t2 = 0 + 0.8333333333
2t + t2 = 0 + 0.8333333333

Combine like terms: 0 + 0.8333333333 = 0.8333333333
2t + t2 = 0.8333333333

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 = 0.8333333333 + 1

Reorder the terms:
1 + 2t + t2 = 0.8333333333 + 1

Combine like terms: 0.8333333333 + 1 = 1.8333333333
1 + 2t + t2 = 1.8333333333

Factor a perfect square on the left side:
(t + 1)(t + 1) = 1.8333333333

Calculate the square root of the right side: 1.354006401

Break this problem into two subproblems by setting 
(t + 1) equal to 1.354006401 and -1.354006401.

Subproblem 1
t + 1 = 1.354006401

Simplifying
t + 1 = 1.354006401

Reorder the terms:
1 + t = 1.354006401

Solving
1 + t = 1.354006401

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 = 1.354006401 + -1

Combine like terms: 1 + -1 = 0
0 + t = 1.354006401 + -1
t = 1.354006401 + -1

Combine like terms: 1.354006401 + -1 = 0.354006401
t = 0.354006401

Simplifying
t = 0.354006401

Subproblem 2
t + 1 = -1.354006401

Simplifying
t + 1 = -1.354006401

Reorder the terms:
1 + t = -1.354006401

Solving
1 + t = -1.354006401

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 = -1.354006401 + -1

Combine like terms: 1 + -1 = 0
0 + t = -1.354006401 + -1
t = -1.354006401 + -1

Combine like terms: -1.354006401 + -1 = -2.354006401
t = -2.354006401

Simplifying
t = -2.354006401

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.354006401, -2.354006401}
Solution
t = {0.354006401, -2.354006401}