20=-16t^2+16t+32

Solution for 20=-16t^2+16t+32 equation:

Simplifying
20 = -16t2 + 16t + 32

Reorder the terms:
20 = 32 + 16t + -16t2

Solving
20 = 32 + 16t + -16t2

Solving for variable 't'.

Combine like terms: 20 + -32 = -12
-12 + -16t + 16t2 = 32 + 16t + -16t2 + -32 + -16t + 16t2

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

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

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

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

Factor out the Greatest Common Factor (GCF), '4'.
4(-3 + -4t + 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}