-16t^2+32t=12

Solution for -16t^2+32t=12 equation:

Simplifying
-16t2 + 32t = 12

Reorder the terms:
32t + -16t2 = 12

Solving
32t + -16t2 = 12

Solving for variable 't'.

Reorder the terms:
-12 + 32t + -16t2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + 32t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-3 + 8t + -4t2) = 0

Factor a trinomial.
4((-3 + 2t)(1 + -2t)) = 0

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

Simplifying
-3 + 2t = 0

Solving
-3 + 2t = 0

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

Add '3' to each side of the equation.
-3 + 3 + 2t = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 2t = 0 + 3
2t = 0 + 3

Combine like terms: 0 + 3 = 3
2t = 3

Divide each side by '2'.
t = 1.5

Simplifying
t = 1.5
Subproblem 2
Set the factor '(1 + -2t)' equal to zero and attempt to solve:

Simplifying
1 + -2t = 0

Solving
1 + -2t = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2t = 0 + -1
-2t = 0 + -1

Combine like terms: 0 + -1 = -1
-2t = -1

Divide each side by '-2'.
t = 0.5

Simplifying
t = 0.5
Solution
t = {1.5, 0.5}