144=-16t^2+64t+80

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Solution for 144=-16t^2+64t+80 equation:


Simplifying
144 = -16t2 + 64t + 80

Reorder the terms:
144 = 80 + 64t + -16t2

Solving
144 = 80 + 64t + -16t2

Solving for variable 't'.

Combine like terms: 144 + -80 = 64
64 + -64t + 16t2 = 80 + 64t + -16t2 + -80 + -64t + 16t2

Reorder the terms:
64 + -64t + 16t2 = 80 + -80 + 64t + -64t + -16t2 + 16t2

Combine like terms: 80 + -80 = 0
64 + -64t + 16t2 = 0 + 64t + -64t + -16t2 + 16t2
64 + -64t + 16t2 = 64t + -64t + -16t2 + 16t2

Combine like terms: 64t + -64t = 0
64 + -64t + 16t2 = 0 + -16t2 + 16t2
64 + -64t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
64 + -64t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(4 + -4t + t2) = 0

Factor a trinomial.
16((2 + -1t)(2 + -1t)) = 0

Ignore the factor 16.

Subproblem 1

Set the factor '(2 + -1t)' equal to zero and attempt to solve: Simplifying 2 + -1t = 0 Solving 2 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t = 0 + -2 -1t = 0 + -2 Combine like terms: 0 + -2 = -2 -1t = -2 Divide each side by '-1'. t = 2 Simplifying t = 2

Subproblem 2

Set the factor '(2 + -1t)' equal to zero and attempt to solve: Simplifying 2 + -1t = 0 Solving 2 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t = 0 + -2 -1t = 0 + -2 Combine like terms: 0 + -2 = -2 -1t = -2 Divide each side by '-1'. t = 2 Simplifying t = 2

Solution

t = {2, 2}

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