152=12+96t-16t^2

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


Simplifying
152 = 12 + 96t + -16t2

Solving
152 = 12 + 96t + -16t2

Solving for variable 't'.

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

Reorder the terms:
140 + -96t + 16t2 = 12 + -12 + 96t + -96t + -16t2 + 16t2

Combine like terms: 12 + -12 = 0
140 + -96t + 16t2 = 0 + 96t + -96t + -16t2 + 16t2
140 + -96t + 16t2 = 96t + -96t + -16t2 + 16t2

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

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

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

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

Ignore the factor 4.

Subproblem 1
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

Subproblem 2
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
Solution
t = {2.5, 3.5}

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