12=-16t^2+32t

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

Simplifying
12 = -16t2 + 32t

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

Solving
12 = 32t + -16t2

Solving for variable 't'.

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

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

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

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

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

Ignore the factor 4.
Subproblem 1
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
Subproblem 2
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
Solution
t = {0.5, 1.5}