15t^2+60t-45=0

Solution for 15t^2+60t-45=0 equation:

Simplifying
15t2 + 60t + -45 = 0

Reorder the terms:
-45 + 60t + 15t2 = 0

Solving
-45 + 60t + 15t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '15'.
15(-3 + 4t + t2) = 0

Ignore the factor 15.
Subproblem 1
Set the factor '(-3 + 4t + t2)' equal to zero and attempt to solve:

Simplifying
-3 + 4t + t2 = 0

Solving
-3 + 4t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 4t + 3 + t2 = 0 + 3

Reorder the terms:
-3 + 3 + 4t + t2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 4t + t2 = 0 + 3
4t + t2 = 0 + 3

Combine like terms: 0 + 3 = 3
4t + t2 = 3

The t term is 4t.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4t + 4 + t2 = 3 + 4

Reorder the terms:
4 + 4t + t2 = 3 + 4

Combine like terms: 3 + 4 = 7
4 + 4t + t2 = 7

Factor a perfect square on the left side:
(t + 2)(t + 2) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(t + 2) equal to 2.645751311 and -2.645751311.

Subproblem 1
t + 2 = 2.645751311

Simplifying
t + 2 = 2.645751311

Reorder the terms:
2 + t = 2.645751311

Solving
2 + t = 2.645751311

Solving for variable 't'.

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

Add '-2' to each side of the equation.
2 + -2 + t = 2.645751311 + -2

Combine like terms: 2 + -2 = 0
0 + t = 2.645751311 + -2
t = 2.645751311 + -2

Combine like terms: 2.645751311 + -2 = 0.645751311
t = 0.645751311

Simplifying
t = 0.645751311

Subproblem 2
t + 2 = -2.645751311

Simplifying
t + 2 = -2.645751311

Reorder the terms:
2 + t = -2.645751311

Solving
2 + t = -2.645751311

Solving for variable 't'.

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

Add '-2' to each side of the equation.
2 + -2 + t = -2.645751311 + -2

Combine like terms: 2 + -2 = 0
0 + t = -2.645751311 + -2
t = -2.645751311 + -2

Combine like terms: -2.645751311 + -2 = -4.645751311
t = -4.645751311

Simplifying
t = -4.645751311

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.645751311, -4.645751311}
Solution
t = {0.645751311, -4.645751311}