0=-16t^2+80t+384

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Solution for 0=-16t^2+80t+384 equation:


Simplifying
0 = -16t2 + 80t + 384

Reorder the terms:
0 = 384 + 80t + -16t2

Solving
0 = 384 + 80t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -384 = -384
-384 + -80t + 16t2 = 384 + 80t + -16t2 + -384 + -80t + 16t2

Reorder the terms:
-384 + -80t + 16t2 = 384 + -384 + 80t + -80t + -16t2 + 16t2

Combine like terms: 384 + -384 = 0
-384 + -80t + 16t2 = 0 + 80t + -80t + -16t2 + 16t2
-384 + -80t + 16t2 = 80t + -80t + -16t2 + 16t2

Combine like terms: 80t + -80t = 0
-384 + -80t + 16t2 = 0 + -16t2 + 16t2
-384 + -80t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-384 + -80t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-24 + -5t + t2) = 0

Factor a trinomial.
16((-3 + -1t)(8 + -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 '(8 + -1t)' equal to zero and attempt to solve: Simplifying 8 + -1t = 0 Solving 8 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1t = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1t = 0 + -8 -1t = 0 + -8 Combine like terms: 0 + -8 = -8 -1t = -8 Divide each side by '-1'. t = 8 Simplifying t = 8

Solution

t = {-3, 8}

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