-16t^2+128t=220

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Solution for -16t^2+128t=220 equation:


Simplifying
-16t2 + 128t = 220

Reorder the terms:
128t + -16t2 = 220

Solving
128t + -16t2 = 220

Solving for variable 't'.

Reorder the terms:
-220 + 128t + -16t2 = 220 + -220

Combine like terms: 220 + -220 = 0
-220 + 128t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-55 + 32t + -4t2) = 0

Factor a trinomial.
4((-11 + 2t)(5 + -2t)) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-11 + 2t)' equal to zero and attempt to solve: Simplifying -11 + 2t = 0 Solving -11 + 2t = 0 Move all terms containing t to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + 2t = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 2t = 0 + 11 2t = 0 + 11 Combine like terms: 0 + 11 = 11 2t = 11 Divide each side by '2'. t = 5.5 Simplifying t = 5.5

Subproblem 2

Set the factor '(5 + -2t)' equal to zero and attempt to solve: Simplifying 5 + -2t = 0 Solving 5 + -2t = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2t = 0 + -5 -2t = 0 + -5 Combine like terms: 0 + -5 = -5 -2t = -5 Divide each side by '-2'. t = 2.5 Simplifying t = 2.5

Solution

t = {5.5, 2.5}

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