0=-16t^2+8t+80

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Solution for 0=-16t^2+8t+80 equation:


Simplifying
0 = -16t2 + 8t + 80

Reorder the terms:
0 = 80 + 8t + -16t2

Solving
0 = 80 + 8t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -80 = -80
-80 + -8t + 16t2 = 80 + 8t + -16t2 + -80 + -8t + 16t2

Reorder the terms:
-80 + -8t + 16t2 = 80 + -80 + 8t + -8t + -16t2 + 16t2

Combine like terms: 80 + -80 = 0
-80 + -8t + 16t2 = 0 + 8t + -8t + -16t2 + 16t2
-80 + -8t + 16t2 = 8t + -8t + -16t2 + 16t2

Combine like terms: 8t + -8t = 0
-80 + -8t + 16t2 = 0 + -16t2 + 16t2
-80 + -8t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-80 + -8t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-10 + -1t + 2t2) = 0

Factor a trinomial.
8((-2 + -1t)(5 + -2t)) = 0

Ignore the factor 8.

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 '(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 = {-2, 2.5}

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