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

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


Simplifying
152 = (-16t2) + 96t + 12

Reorder the terms:
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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