50t^2+100t-60=0

Solution for 50t^2+100t-60=0 equation:

Simplifying
50t2 + 100t + -60 = 0

Reorder the terms:
-60 + 100t + 50t2 = 0

Solving
-60 + 100t + 50t2 = 0

Solving for variable 't'.

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

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

Simplifying
-6 + 10t + 5t2 = 0

Solving
-6 + 10t + 5t2 = 0

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

Divide each side by '5'.
-1.2 + 2t + t2 = 0

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + 2t + 1.2 + t2 = 0 + 1.2

Reorder the terms:
-1.2 + 1.2 + 2t + t2 = 0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + 2t + t2 = 0 + 1.2
2t + t2 = 0 + 1.2

Combine like terms: 0 + 1.2 = 1.2
2t + t2 = 1.2

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 = 1.2 + 1

Reorder the terms:
1 + 2t + t2 = 1.2 + 1

Combine like terms: 1.2 + 1 = 2.2
1 + 2t + t2 = 2.2

Factor a perfect square on the left side:
(t + 1)(t + 1) = 2.2

Calculate the square root of the right side: 1.483239697

Break this problem into two subproblems by setting 
(t + 1) equal to 1.483239697 and -1.483239697.

Subproblem 1
t + 1 = 1.483239697

Simplifying
t + 1 = 1.483239697

Reorder the terms:
1 + t = 1.483239697

Solving
1 + t = 1.483239697

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 = 1.483239697 + -1

Combine like terms: 1 + -1 = 0
0 + t = 1.483239697 + -1
t = 1.483239697 + -1

Combine like terms: 1.483239697 + -1 = 0.483239697
t = 0.483239697

Simplifying
t = 0.483239697

Subproblem 2
t + 1 = -1.483239697

Simplifying
t + 1 = -1.483239697

Reorder the terms:
1 + t = -1.483239697

Solving
1 + t = -1.483239697

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 = -1.483239697 + -1

Combine like terms: 1 + -1 = 0
0 + t = -1.483239697 + -1
t = -1.483239697 + -1

Combine like terms: -1.483239697 + -1 = -2.483239697
t = -2.483239697

Simplifying
t = -2.483239697

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.483239697, -2.483239697}
Solution
t = {0.483239697, -2.483239697}