144=96t-16t^2

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Solution for 144=96t-16t^2 equation:


Simplifying
144 = 96t + -16t2

Solving
144 = 96t + -16t2

Solving for variable 't'.

Reorder the terms:
144 + -96t + 16t2 = 96t + -96t + -16t2 + 16t2

Combine like terms: 96t + -96t = 0
144 + -96t + 16t2 = 0 + -16t2 + 16t2
144 + -96t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
144 + -96t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(9 + -6t + t2) = 0

Factor a trinomial.
16((3 + -1t)(3 + -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 '(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

Solution

t = {3, 3}

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