96=-16t^2+116t+96

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Solution for 96=-16t^2+116t+96 equation:


Simplifying
96 = -16t2 + 116t + 96

Reorder the terms:
96 = 96 + 116t + -16t2

Add '-96' to each side of the equation.
96 + -96 = 96 + 116t + -96 + -16t2

Combine like terms: 96 + -96 = 0
0 = 96 + 116t + -96 + -16t2

Reorder the terms:
0 = 96 + -96 + 116t + -16t2

Combine like terms: 96 + -96 = 0
0 = 0 + 116t + -16t2
0 = 116t + -16t2

Solving
0 = 116t + -16t2

Solving for variable 't'.
Remove the zero:
-116t + 16t2 = 116t + -16t2 + -116t + 16t2

Reorder the terms:
-116t + 16t2 = 116t + -116t + -16t2 + 16t2

Combine like terms: 116t + -116t = 0
-116t + 16t2 = 0 + -16t2 + 16t2
-116t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-116t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '4t'.
4t(-29 + 4t) = 0

Ignore the factor 4.

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 '(-29 + 4t)' equal to zero and attempt to solve: Simplifying -29 + 4t = 0 Solving -29 + 4t = 0 Move all terms containing t to the left, all other terms to the right. Add '29' to each side of the equation. -29 + 29 + 4t = 0 + 29 Combine like terms: -29 + 29 = 0 0 + 4t = 0 + 29 4t = 0 + 29 Combine like terms: 0 + 29 = 29 4t = 29 Divide each side by '4'. t = 7.25 Simplifying t = 7.25

Solution

t = {0, 7.25}

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