h(0)=-16t^2+96t

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Solution for h(0)=-16t^2+96t equation:


Simplifying
h(0) = -16t2 + 96t

Reorder the terms for easier multiplication:
0h = -16t2 + 96t

Anything times zero is zero.
0h = -16t2 + 96t

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

Solving
0 = 96t + -16t2

Solving for variable 't'.
Remove the zero:
-96t + 16t2 = 96t + -16t2 + -96t + 16t2

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

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

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

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

Ignore the factor 16.

Subproblem 1

Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0

Subproblem 2

Set the factor '(-6 + t)' equal to zero and attempt to solve: Simplifying -6 + t = 0 Solving -6 + t = 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 + t = 0 + 6 Combine like terms: -6 + 6 = 0 0 + t = 0 + 6 t = 0 + 6 Combine like terms: 0 + 6 = 6 t = 6 Simplifying t = 6

Solution

t = {0, 6}

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