(0.5)32t^2+16t=96

Solution for (0.5)32t^2+16t=96 equation:

Simplifying
(0.5) * 32t2 + 16t = 96

Multiply 0.5 * 32
16t2 + 16t = 96

Reorder the terms:
16t + 16t2 = 96

Solving
16t + 16t2 = 96

Solving for variable 't'.

Reorder the terms:
-96 + 16t + 16t2 = 96 + -96

Combine like terms: 96 + -96 = 0
-96 + 16t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-6 + t + t2) = 0

Factor a trinomial.
16((-3 + -1t)(2 + -1t)) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(-3 + -1t)' equal to zero and attempt to solve:

Simplifying
-3 + -1t = 0

Solving
-3 + -1t = 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 + -1t = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1t = 0 + 3
-1t = 0 + 3

Combine like terms: 0 + 3 = 3
-1t = 3

Divide each side by '-1'.
t = -3

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

Simplifying
2 + -1t = 0

Solving
2 + -1t = 0

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

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

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

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

Divide each side by '-1'.
t = 2

Simplifying
t = 2
Solution
t = {-3, 2}