-16t^2+144t=288

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Solution for -16t^2+144t=288 equation:


Simplifying
-16t2 + 144t = 288

Reorder the terms:
144t + -16t2 = 288

Solving
144t + -16t2 = 288

Solving for variable 't'.

Reorder the terms:
-288 + 144t + -16t2 = 288 + -288

Combine like terms: 288 + -288 = 0
-288 + 144t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-18 + 9t + -1t2) = 0

Factor a trinomial.
16((-6 + t)(3 + -1t)) = 0

Ignore the factor 16.

Subproblem 1

Set the factor '(-6 + t)' equal to zero and attempt to solve: Simplifying -6 + t = 0 Solving -6 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + t = 0 + 6 Combine like terms: -6 + 6 = 0 0 + t = 0 + 6 t = 0 + 6 Combine like terms: 0 + 6 = 6 t = 6 Simplifying t = 6

Subproblem 2

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

Solution

t = {6, 3}

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