-16t^2+96t+12=152

Solution for -16t^2+96t+12=152 equation:

Simplifying
-16t2 + 96t + 12 = 152

Reorder the terms:
12 + 96t + -16t2 = 152

Solving
12 + 96t + -16t2 = 152

Solving for variable 't'.

Reorder the terms:
12 + -152 + 96t + -16t2 = 152 + -152

Combine like terms: 12 + -152 = -140
-140 + 96t + -16t2 = 152 + -152

Combine like terms: 152 + -152 = 0
-140 + 96t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-35 + 24t + -4t2) = 0

Factor a trinomial.
4((-7 + 2t)(5 + -2t)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-7 + 2t)' equal to zero and attempt to solve:

Simplifying
-7 + 2t = 0

Solving
-7 + 2t = 0

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

Add '7' to each side of the equation.
-7 + 7 + 2t = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 2t = 0 + 7
2t = 0 + 7

Combine like terms: 0 + 7 = 7
2t = 7

Divide each side by '2'.
t = 3.5

Simplifying
t = 3.5
Subproblem 2
Set the factor '(5 + -2t)' equal to zero and attempt to solve:

Simplifying
5 + -2t = 0

Solving
5 + -2t = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2t = 0 + -5
-2t = 0 + -5

Combine like terms: 0 + -5 = -5
-2t = -5

Divide each side by '-2'.
t = 2.5

Simplifying
t = 2.5
Solution
t = {3.5, 2.5}