0=-15t^2-18t+12

Solution for 0=-15t^2-18t+12 equation:

Simplifying
0 = -15t2 + -18t + 12

Reorder the terms:
0 = 12 + -18t + -15t2

Solving
0 = 12 + -18t + -15t2

Solving for variable 't'.

Combine like terms: 0 + -12 = -12
-12 + 18t + 15t2 = 12 + -18t + -15t2 + -12 + 18t + 15t2

Reorder the terms:
-12 + 18t + 15t2 = 12 + -12 + -18t + 18t + -15t2 + 15t2

Combine like terms: 12 + -12 = 0
-12 + 18t + 15t2 = 0 + -18t + 18t + -15t2 + 15t2
-12 + 18t + 15t2 = -18t + 18t + -15t2 + 15t2

Combine like terms: -18t + 18t = 0
-12 + 18t + 15t2 = 0 + -15t2 + 15t2
-12 + 18t + 15t2 = -15t2 + 15t2

Combine like terms: -15t2 + 15t2 = 0
-12 + 18t + 15t2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + 6t + 5t2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-4 + 6t + 5t2)' equal to zero and attempt to solve:

Simplifying
-4 + 6t + 5t2 = 0

Solving
-4 + 6t + 5t2 = 0

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

Divide each side by '5'.
-0.8 + 1.2t + t2 = 0

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + 1.2t + 0.8 + t2 = 0 + 0.8

Reorder the terms:
-0.8 + 0.8 + 1.2t + t2 = 0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + 1.2t + t2 = 0 + 0.8
1.2t + t2 = 0 + 0.8

Combine like terms: 0 + 0.8 = 0.8
1.2t + t2 = 0.8

The t term is 1.2t.  Take half its coefficient (0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
1.2t + 0.36 + t2 = 0.8 + 0.36

Reorder the terms:
0.36 + 1.2t + t2 = 0.8 + 0.36

Combine like terms: 0.8 + 0.36 = 1.16
0.36 + 1.2t + t2 = 1.16

Factor a perfect square on the left side:
(t + 0.6)(t + 0.6) = 1.16

Calculate the square root of the right side: 1.077032961

Break this problem into two subproblems by setting 
(t + 0.6) equal to 1.077032961 and -1.077032961.

Subproblem 1
t + 0.6 = 1.077032961

Simplifying
t + 0.6 = 1.077032961

Reorder the terms:
0.6 + t = 1.077032961

Solving
0.6 + t = 1.077032961

Solving for variable 't'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + t = 1.077032961 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + t = 1.077032961 + -0.6
t = 1.077032961 + -0.6

Combine like terms: 1.077032961 + -0.6 = 0.477032961
t = 0.477032961

Simplifying
t = 0.477032961

Subproblem 2
t + 0.6 = -1.077032961

Simplifying
t + 0.6 = -1.077032961

Reorder the terms:
0.6 + t = -1.077032961

Solving
0.6 + t = -1.077032961

Solving for variable 't'.

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

Add '-0.6' to each side of the equation.
0.6 + -0.6 + t = -1.077032961 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + t = -1.077032961 + -0.6
t = -1.077032961 + -0.6

Combine like terms: -1.077032961 + -0.6 = -1.677032961
t = -1.677032961

Simplifying
t = -1.677032961

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.477032961, -1.677032961}
Solution
t = {0.477032961, -1.677032961}