12t^2+6t-15=0

Solution for 12t^2+6t-15=0 equation:

Simplifying
12t2 + 6t + -15 = 0

Reorder the terms:
-15 + 6t + 12t2 = 0

Solving
-15 + 6t + 12t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + 2t + 4t2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-5 + 2t + 4t2)' equal to zero and attempt to solve:

Simplifying
-5 + 2t + 4t2 = 0

Solving
-5 + 2t + 4t2 = 0

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

Divide each side by '4'.
-1.25 + 0.5t + t2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + 0.5t + 1.25 + t2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + 0.5t + t2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + 0.5t + t2 = 0 + 1.25
0.5t + t2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
0.5t + t2 = 1.25

The t term is 0.5t.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5t + 0.0625 + t2 = 1.25 + 0.0625

Reorder the terms:
0.0625 + 0.5t + t2 = 1.25 + 0.0625

Combine like terms: 1.25 + 0.0625 = 1.3125
0.0625 + 0.5t + t2 = 1.3125

Factor a perfect square on the left side:
(t + 0.25)(t + 0.25) = 1.3125

Calculate the square root of the right side: 1.145643924

Break this problem into two subproblems by setting 
(t + 0.25) equal to 1.145643924 and -1.145643924.

Subproblem 1
t + 0.25 = 1.145643924

Simplifying
t + 0.25 = 1.145643924

Reorder the terms:
0.25 + t = 1.145643924

Solving
0.25 + t = 1.145643924

Solving for variable 't'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + t = 1.145643924 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + t = 1.145643924 + -0.25
t = 1.145643924 + -0.25

Combine like terms: 1.145643924 + -0.25 = 0.895643924
t = 0.895643924

Simplifying
t = 0.895643924

Subproblem 2
t + 0.25 = -1.145643924

Simplifying
t + 0.25 = -1.145643924

Reorder the terms:
0.25 + t = -1.145643924

Solving
0.25 + t = -1.145643924

Solving for variable 't'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + t = -1.145643924 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + t = -1.145643924 + -0.25
t = -1.145643924 + -0.25

Combine like terms: -1.145643924 + -0.25 = -1.395643924
t = -1.395643924

Simplifying
t = -1.395643924

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.895643924, -1.395643924}
Solution
t = {0.895643924, -1.395643924}