15t^2+75t+75=0

Solution for 15t^2+75t+75=0 equation:

Simplifying
15t2 + 75t + 75 = 0

Reorder the terms:
75 + 75t + 15t2 = 0

Solving
75 + 75t + 15t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '15'.
15(5 + 5t + t2) = 0

Ignore the factor 15.
Subproblem 1
Set the factor '(5 + 5t + t2)' equal to zero and attempt to solve:

Simplifying
5 + 5t + t2 = 0

Solving
5 + 5t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 5t + -5 + t2 = 0 + -5

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

Combine like terms: 5 + -5 = 0
0 + 5t + t2 = 0 + -5
5t + t2 = 0 + -5

Combine like terms: 0 + -5 = -5
5t + t2 = -5

The t term is 5t.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5t + 6.25 + t2 = -5 + 6.25

Reorder the terms:
6.25 + 5t + t2 = -5 + 6.25

Combine like terms: -5 + 6.25 = 1.25
6.25 + 5t + t2 = 1.25

Factor a perfect square on the left side:
(t + 2.5)(t + 2.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(t + 2.5) equal to 1.118033989 and -1.118033989.

Subproblem 1
t + 2.5 = 1.118033989

Simplifying
t + 2.5 = 1.118033989

Reorder the terms:
2.5 + t = 1.118033989

Solving
2.5 + t = 1.118033989

Solving for variable 't'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + t = 1.118033989 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + t = 1.118033989 + -2.5
t = 1.118033989 + -2.5

Combine like terms: 1.118033989 + -2.5 = -1.381966011
t = -1.381966011

Simplifying
t = -1.381966011

Subproblem 2
t + 2.5 = -1.118033989

Simplifying
t + 2.5 = -1.118033989

Reorder the terms:
2.5 + t = -1.118033989

Solving
2.5 + t = -1.118033989

Solving for variable 't'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + t = -1.118033989 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + t = -1.118033989 + -2.5
t = -1.118033989 + -2.5

Combine like terms: -1.118033989 + -2.5 = -3.618033989
t = -3.618033989

Simplifying
t = -3.618033989

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-1.381966011, -3.618033989}
Solution
t = {-1.381966011, -3.618033989}