-16t^2+72t=32

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

Simplifying
-16t2 + 72t = 32

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

Solving
72t + -16t2 = 32

Solving for variable 't'.

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

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

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

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

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

Simplifying
-4 + t = 0

Solving
-4 + t = 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 + t = 0 + 4

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

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

Simplifying
t = 4
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 = {4, 0.5}