=-16t^2+96t+1152

Solution for =-16t^2+96t+1152 equation:

Simplifying
0 = -16t2 + 96t + 1152

Reorder the terms:
0 = 1152 + 96t + -16t2

Solving
0 = 1152 + 96t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -1152 = -1152
-1152 + -96t + 16t2 = 1152 + 96t + -16t2 + -1152 + -96t + 16t2

Reorder the terms:
-1152 + -96t + 16t2 = 1152 + -1152 + 96t + -96t + -16t2 + 16t2

Combine like terms: 1152 + -1152 = 0
-1152 + -96t + 16t2 = 0 + 96t + -96t + -16t2 + 16t2
-1152 + -96t + 16t2 = 96t + -96t + -16t2 + 16t2

Combine like terms: 96t + -96t = 0
-1152 + -96t + 16t2 = 0 + -16t2 + 16t2
-1152 + -96t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-1152 + -96t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-72 + -6t + t2) = 0

Factor a trinomial.
16((-6 + -1t)(12 + -1t)) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(-6 + -1t)' equal to zero and attempt to solve:

Simplifying
-6 + -1t = 0

Solving
-6 + -1t = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1t = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1t = 0 + 6
-1t = 0 + 6

Combine like terms: 0 + 6 = 6
-1t = 6

Divide each side by '-1'.
t = -6

Simplifying
t = -6
Subproblem 2
Set the factor '(12 + -1t)' equal to zero and attempt to solve:

Simplifying
12 + -1t = 0

Solving
12 + -1t = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1t = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1t = 0 + -12
-1t = 0 + -12

Combine like terms: 0 + -12 = -12
-1t = -12

Divide each side by '-1'.
t = 12

Simplifying
t = 12
Solution
t = {-6, 12}