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Simplifying 432 = -16t2 + 64t + 512 Reorder the terms: 432 = 512 + 64t + -16t2 Solving 432 = 512 + 64t + -16t2 Solving for variable 't'. Combine like terms: 432 + -512 = -80 -80 + -64t + 16t2 = 512 + 64t + -16t2 + -512 + -64t + 16t2 Reorder the terms: -80 + -64t + 16t2 = 512 + -512 + 64t + -64t + -16t2 + 16t2 Combine like terms: 512 + -512 = 0 -80 + -64t + 16t2 = 0 + 64t + -64t + -16t2 + 16t2 -80 + -64t + 16t2 = 64t + -64t + -16t2 + 16t2 Combine like terms: 64t + -64t = 0 -80 + -64t + 16t2 = 0 + -16t2 + 16t2 -80 + -64t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -80 + -64t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-5 + -4t + t2) = 0 Factor a trinomial. 16((-1 + -1t)(5 + -1t)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-1 + -1t)' equal to zero and attempt to solve: Simplifying -1 + -1t = 0 Solving -1 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1t = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1t = 0 + 1 -1t = 0 + 1 Combine like terms: 0 + 1 = 1 -1t = 1 Divide each side by '-1'. t = -1 Simplifying t = -1Subproblem 2
Set the factor '(5 + -1t)' equal to zero and attempt to solve: Simplifying 5 + -1t = 0 Solving 5 + -1t = 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 + -1t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1t = 0 + -5 -1t = 0 + -5 Combine like terms: 0 + -5 = -5 -1t = -5 Divide each side by '-1'. t = 5 Simplifying t = 5Solution
t = {-1, 5}
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