6t^2-15t-12=0

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

Simplifying
6t2 + -15t + -12 = 0

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

Solving
-12 + -15t + 6t2 = 0

Solving for variable 't'.

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

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

Simplifying
-4 + -5t + 2t2 = 0

Solving
-4 + -5t + 2t2 = 0

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

Divide each side by '2'.
-2 + -2.5t + t2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -2.5t + 2 + t2 = 0 + 2

Reorder the terms:
-2 + 2 + -2.5t + t2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -2.5t + t2 = 0 + 2
-2.5t + t2 = 0 + 2

Combine like terms: 0 + 2 = 2
-2.5t + t2 = 2

The t term is -2.5t.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5t + 1.5625 + t2 = 2 + 1.5625

Reorder the terms:
1.5625 + -2.5t + t2 = 2 + 1.5625

Combine like terms: 2 + 1.5625 = 3.5625
1.5625 + -2.5t + t2 = 3.5625

Factor a perfect square on the left side:
(t + -1.25)(t + -1.25) = 3.5625

Calculate the square root of the right side: 1.887458609

Break this problem into two subproblems by setting 
(t + -1.25) equal to 1.887458609 and -1.887458609.

Subproblem 1
t + -1.25 = 1.887458609

Simplifying
t + -1.25 = 1.887458609

Reorder the terms:
-1.25 + t = 1.887458609

Solving
-1.25 + t = 1.887458609

Solving for variable 't'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + t = 1.887458609 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + t = 1.887458609 + 1.25
t = 1.887458609 + 1.25

Combine like terms: 1.887458609 + 1.25 = 3.137458609
t = 3.137458609

Simplifying
t = 3.137458609

Subproblem 2
t + -1.25 = -1.887458609

Simplifying
t + -1.25 = -1.887458609

Reorder the terms:
-1.25 + t = -1.887458609

Solving
-1.25 + t = -1.887458609

Solving for variable 't'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + t = -1.887458609 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + t = -1.887458609 + 1.25
t = -1.887458609 + 1.25

Combine like terms: -1.887458609 + 1.25 = -0.637458609
t = -0.637458609

Simplifying
t = -0.637458609

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.137458609, -0.637458609}
Solution
t = {3.137458609, -0.637458609}