32=-16t^2+72t

Solution for 32=-16t^2+72t equation:

Simplifying
32 = -16t2 + 72t

Reorder the terms:
32 = 72t + -16t2

Solving
32 = 72t + -16t2

Solving for variable 't'.

Reorder the terms:
32 + -72t + 16t2 = 72t + -72t + -16t2 + 16t2

Combine like terms: 72t + -72t = 0
32 + -72t + 16t2 = 0 + -16t2 + 16t2
32 + -72t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
32 + -72t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(4 + -9t + 2t2) = 0

Factor a trinomial.
8((1 + -2t)(4 + -1t)) = 0

Ignore the factor 8.
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 '(4 + -1t)' equal to zero and attempt to solve:

Simplifying
4 + -1t = 0

Solving
4 + -1t = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1t = 0 + -4
-1t = 0 + -4

Combine like terms: 0 + -4 = -4
-1t = -4

Divide each side by '-1'.
t = 4

Simplifying
t = 4
Solution
t = {0.5, 4}