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Simplifying 0 = -16t2 + 64t + 192 Reorder the terms: 0 = 192 + 64t + -16t2 Solving 0 = 192 + 64t + -16t2 Solving for variable 't'. Combine like terms: 0 + -192 = -192 -192 + -64t + 16t2 = 192 + 64t + -16t2 + -192 + -64t + 16t2 Reorder the terms: -192 + -64t + 16t2 = 192 + -192 + 64t + -64t + -16t2 + 16t2 Combine like terms: 192 + -192 = 0 -192 + -64t + 16t2 = 0 + 64t + -64t + -16t2 + 16t2 -192 + -64t + 16t2 = 64t + -64t + -16t2 + 16t2 Combine like terms: 64t + -64t = 0 -192 + -64t + 16t2 = 0 + -16t2 + 16t2 -192 + -64t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -192 + -64t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-12 + -4t + t2) = 0 Factor a trinomial. 16((-2 + -1t)(6 + -1t)) = 0 Ignore the factor 16.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 = -2Subproblem 2
Set the factor '(6 + -1t)' equal to zero and attempt to solve: Simplifying 6 + -1t = 0 Solving 6 + -1t = 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 + -1t = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1t = 0 + -6 -1t = 0 + -6 Combine like terms: 0 + -6 = -6 -1t = -6 Divide each side by '-1'. t = 6 Simplifying t = 6Solution
t = {-2, 6}
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