-16t^2+30t-12=0

Solution for -16t^2+30t-12=0 equation:

Simplifying
-16t2 + 30t + -12 = 0

Reorder the terms:
-12 + 30t + -16t2 = 0

Solving
-12 + 30t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 15t + -8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + 15t + -8t2)' equal to zero and attempt to solve:

Simplifying
-6 + 15t + -8t2 = 0

Solving
-6 + 15t + -8t2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
0.75 + -1.875t + t2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + -1.875t + -0.75 + t2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + -1.875t + t2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + -1.875t + t2 = 0 + -0.75
-1.875t + t2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
-1.875t + t2 = -0.75

The t term is -1.875t.  Take half its coefficient (-0.9375).
Square it (0.87890625) and add it to both sides.

Add '0.87890625' to each side of the equation.
-1.875t + 0.87890625 + t2 = -0.75 + 0.87890625

Reorder the terms:
0.87890625 + -1.875t + t2 = -0.75 + 0.87890625

Combine like terms: -0.75 + 0.87890625 = 0.12890625
0.87890625 + -1.875t + t2 = 0.12890625

Factor a perfect square on the left side:
(t + -0.9375)(t + -0.9375) = 0.12890625

Calculate the square root of the right side: 0.359035165

Break this problem into two subproblems by setting 
(t + -0.9375) equal to 0.359035165 and -0.359035165.

Subproblem 1
t + -0.9375 = 0.359035165

Simplifying
t + -0.9375 = 0.359035165

Reorder the terms:
-0.9375 + t = 0.359035165

Solving
-0.9375 + t = 0.359035165

Solving for variable 't'.

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

Add '0.9375' to each side of the equation.
-0.9375 + 0.9375 + t = 0.359035165 + 0.9375

Combine like terms: -0.9375 + 0.9375 = 0.0000
0.0000 + t = 0.359035165 + 0.9375
t = 0.359035165 + 0.9375

Combine like terms: 0.359035165 + 0.9375 = 1.296535165
t = 1.296535165

Simplifying
t = 1.296535165

Subproblem 2
t + -0.9375 = -0.359035165

Simplifying
t + -0.9375 = -0.359035165

Reorder the terms:
-0.9375 + t = -0.359035165

Solving
-0.9375 + t = -0.359035165

Solving for variable 't'.

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

Add '0.9375' to each side of the equation.
-0.9375 + 0.9375 + t = -0.359035165 + 0.9375

Combine like terms: -0.9375 + 0.9375 = 0.0000
0.0000 + t = -0.359035165 + 0.9375
t = -0.359035165 + 0.9375

Combine like terms: -0.359035165 + 0.9375 = 0.578464835
t = 0.578464835

Simplifying
t = 0.578464835

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.296535165, 0.578464835}
Solution
t = {1.296535165, 0.578464835}