261=-16t^2+128t+5

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Solution for 261=-16t^2+128t+5 equation:


Simplifying
261 = -16t2 + 128t + 5

Reorder the terms:
261 = 5 + 128t + -16t2

Solving
261 = 5 + 128t + -16t2

Solving for variable 't'.

Combine like terms: 261 + -5 = 256
256 + -128t + 16t2 = 5 + 128t + -16t2 + -5 + -128t + 16t2

Reorder the terms:
256 + -128t + 16t2 = 5 + -5 + 128t + -128t + -16t2 + 16t2

Combine like terms: 5 + -5 = 0
256 + -128t + 16t2 = 0 + 128t + -128t + -16t2 + 16t2
256 + -128t + 16t2 = 128t + -128t + -16t2 + 16t2

Combine like terms: 128t + -128t = 0
256 + -128t + 16t2 = 0 + -16t2 + 16t2
256 + -128t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
256 + -128t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(16 + -8t + t2) = 0

Factor a trinomial.
16((4 + -1t)(4 + -1t)) = 0

Ignore the factor 16.

Subproblem 1

Set the factor '(4 + -1t)' equal to zero and attempt to solve: Simplifying 4 + -1t = 0 Solving 4 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1t = 0 + -4 -1t = 0 + -4 Combine like terms: 0 + -4 = -4 -1t = -4 Divide each side by '-1'. t = 4 Simplifying t = 4

Subproblem 2

Set the factor '(4 + -1t)' equal to zero and attempt to solve: Simplifying 4 + -1t = 0 Solving 4 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1t = 0 + -4 -1t = 0 + -4 Combine like terms: 0 + -4 = -4 -1t = -4 Divide each side by '-1'. t = 4 Simplifying t = 4

Solution

t = {4, 4}

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