-16t^2+6t+12=6

Solution for -16t^2+6t+12=6 equation:

Simplifying
-16t2 + 6t + 12 = 6

Reorder the terms:
12 + 6t + -16t2 = 6

Solving
12 + 6t + -16t2 = 6

Solving for variable 't'.

Reorder the terms:
12 + -6 + 6t + -16t2 = 6 + -6

Combine like terms: 12 + -6 = 6
6 + 6t + -16t2 = 6 + -6

Combine like terms: 6 + -6 = 0
6 + 6t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 3t + -8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + 3t + -8t2)' equal to zero and attempt to solve:

Simplifying
3 + 3t + -8t2 = 0

Solving
3 + 3t + -8t2 = 0

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

Divide each side by '-8'.
-0.375 + -0.375t + t2 = 0

Move the constant term to the right:

Add '0.375' to each side of the equation.
-0.375 + -0.375t + 0.375 + t2 = 0 + 0.375

Reorder the terms:
-0.375 + 0.375 + -0.375t + t2 = 0 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + -0.375t + t2 = 0 + 0.375
-0.375t + t2 = 0 + 0.375

Combine like terms: 0 + 0.375 = 0.375
-0.375t + t2 = 0.375

The t term is -0.375t.  Take half its coefficient (-0.1875).
Square it (0.03515625) and add it to both sides.

Add '0.03515625' to each side of the equation.
-0.375t + 0.03515625 + t2 = 0.375 + 0.03515625

Reorder the terms:
0.03515625 + -0.375t + t2 = 0.375 + 0.03515625

Combine like terms: 0.375 + 0.03515625 = 0.41015625
0.03515625 + -0.375t + t2 = 0.41015625

Factor a perfect square on the left side:
(t + -0.1875)(t + -0.1875) = 0.41015625

Calculate the square root of the right side: 0.640434423

Break this problem into two subproblems by setting 
(t + -0.1875) equal to 0.640434423 and -0.640434423.

Subproblem 1
t + -0.1875 = 0.640434423

Simplifying
t + -0.1875 = 0.640434423

Reorder the terms:
-0.1875 + t = 0.640434423

Solving
-0.1875 + t = 0.640434423

Solving for variable 't'.

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

Add '0.1875' to each side of the equation.
-0.1875 + 0.1875 + t = 0.640434423 + 0.1875

Combine like terms: -0.1875 + 0.1875 = 0.0000
0.0000 + t = 0.640434423 + 0.1875
t = 0.640434423 + 0.1875

Combine like terms: 0.640434423 + 0.1875 = 0.827934423
t = 0.827934423

Simplifying
t = 0.827934423

Subproblem 2
t + -0.1875 = -0.640434423

Simplifying
t + -0.1875 = -0.640434423

Reorder the terms:
-0.1875 + t = -0.640434423

Solving
-0.1875 + t = -0.640434423

Solving for variable 't'.

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

Add '0.1875' to each side of the equation.
-0.1875 + 0.1875 + t = -0.640434423 + 0.1875

Combine like terms: -0.1875 + 0.1875 = 0.0000
0.0000 + t = -0.640434423 + 0.1875
t = -0.640434423 + 0.1875

Combine like terms: -0.640434423 + 0.1875 = -0.452934423
t = -0.452934423

Simplifying
t = -0.452934423

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.827934423, -0.452934423}
Solution
t = {0.827934423, -0.452934423}