-5t^2-5t+180=0

Solution for -5t^2-5t+180=0 equation:

Simplifying
-5t2 + -5t + 180 = 0

Reorder the terms:
180 + -5t + -5t2 = 0

Solving
180 + -5t + -5t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '5'.
5(36 + -1t + -1t2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(36 + -1t + -1t2)' equal to zero and attempt to solve:

Simplifying
36 + -1t + -1t2 = 0

Solving
36 + -1t + -1t2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-36 + t + t2 = 0

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + t + 36 + t2 = 0 + 36

Reorder the terms:
-36 + 36 + t + t2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + t + t2 = 0 + 36
t + t2 = 0 + 36

Combine like terms: 0 + 36 = 36
t + t2 = 36

The t term is t.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + t2 = 36 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + t2 = 36 + 0.25

Combine like terms: 36 + 0.25 = 36.25
1.25 + t2 = 36.25

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = 36.25

Calculate the square root of the right side: 6.020797289

Break this problem into two subproblems by setting 
(t + 0.5) equal to 6.020797289 and -6.020797289.

Subproblem 1
t + 0.5 = 6.020797289

Simplifying
t + 0.5 = 6.020797289

Reorder the terms:
0.5 + t = 6.020797289

Solving
0.5 + t = 6.020797289

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = 6.020797289 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = 6.020797289 + -0.5
t = 6.020797289 + -0.5

Combine like terms: 6.020797289 + -0.5 = 5.520797289
t = 5.520797289

Simplifying
t = 5.520797289

Subproblem 2
t + 0.5 = -6.020797289

Simplifying
t + 0.5 = -6.020797289

Reorder the terms:
0.5 + t = -6.020797289

Solving
0.5 + t = -6.020797289

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = -6.020797289 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = -6.020797289 + -0.5
t = -6.020797289 + -0.5

Combine like terms: -6.020797289 + -0.5 = -6.520797289
t = -6.520797289

Simplifying
t = -6.520797289

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {5.520797289, -6.520797289}
Solution
t = {5.520797289, -6.520797289}