15t^2+90t-75=0

Solution for 15t^2+90t-75=0 equation:

Simplifying
15t2 + 90t + -75 = 0

Reorder the terms:
-75 + 90t + 15t2 = 0

Solving
-75 + 90t + 15t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '15'.
15(-5 + 6t + t2) = 0

Ignore the factor 15.
Subproblem 1
Set the factor '(-5 + 6t + t2)' equal to zero and attempt to solve:

Simplifying
-5 + 6t + t2 = 0

Solving
-5 + 6t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 6t + 5 + t2 = 0 + 5

Reorder the terms:
-5 + 5 + 6t + t2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 6t + t2 = 0 + 5
6t + t2 = 0 + 5

Combine like terms: 0 + 5 = 5
6t + t2 = 5

The t term is 6t.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6t + 9 + t2 = 5 + 9

Reorder the terms:
9 + 6t + t2 = 5 + 9

Combine like terms: 5 + 9 = 14
9 + 6t + t2 = 14

Factor a perfect square on the left side:
(t + 3)(t + 3) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(t + 3) equal to 3.741657387 and -3.741657387.

Subproblem 1
t + 3 = 3.741657387

Simplifying
t + 3 = 3.741657387

Reorder the terms:
3 + t = 3.741657387

Solving
3 + t = 3.741657387

Solving for variable 't'.

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

Add '-3' to each side of the equation.
3 + -3 + t = 3.741657387 + -3

Combine like terms: 3 + -3 = 0
0 + t = 3.741657387 + -3
t = 3.741657387 + -3

Combine like terms: 3.741657387 + -3 = 0.741657387
t = 0.741657387

Simplifying
t = 0.741657387

Subproblem 2
t + 3 = -3.741657387

Simplifying
t + 3 = -3.741657387

Reorder the terms:
3 + t = -3.741657387

Solving
3 + t = -3.741657387

Solving for variable 't'.

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

Add '-3' to each side of the equation.
3 + -3 + t = -3.741657387 + -3

Combine like terms: 3 + -3 = 0
0 + t = -3.741657387 + -3
t = -3.741657387 + -3

Combine like terms: -3.741657387 + -3 = -6.741657387
t = -6.741657387

Simplifying
t = -6.741657387

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.741657387, -6.741657387}
Solution
t = {0.741657387, -6.741657387}