0=-16t^2+96t+432

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Solution for 0=-16t^2+96t+432 equation: 


Simplifying
0 = -16t2 + 96t + 432

Reorder the terms:
0 = 432 + 96t + -16t2

Solving
0 = 432 + 96t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -432 = -432
-432 + -96t + 16t2 = 432 + 96t + -16t2 + -432 + -96t + 16t2

Reorder the terms:
-432 + -96t + 16t2 = 432 + -432 + 96t + -96t + -16t2 + 16t2

Combine like terms: 432 + -432 = 0
-432 + -96t + 16t2 = 0 + 96t + -96t + -16t2 + 16t2
-432 + -96t + 16t2 = 96t + -96t + -16t2 + 16t2

Combine like terms: 96t + -96t = 0
-432 + -96t + 16t2 = 0 + -16t2 + 16t2
-432 + -96t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-432 + -96t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-27 + -6t + t2) = 0

Factor a trinomial.
16((-3 + -1t)(9 + -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 '(9 + -1t)' equal to zero and attempt to solve:

Simplifying
9 + -1t = 0

Solving
9 + -1t = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1t = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1t = 0 + -9
-1t = 0 + -9

Combine like terms: 0 + -9 = -9
-1t = -9

Divide each side by '-1'.
t = 9

Simplifying
t = 9
Solution
t = {-3, 9}

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