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Simplifying 0 = -16t2 + 112t + 960 Reorder the terms: 0 = 960 + 112t + -16t2 Solving 0 = 960 + 112t + -16t2 Solving for variable 't'. Combine like terms: 0 + -960 = -960 -960 + -112t + 16t2 = 960 + 112t + -16t2 + -960 + -112t + 16t2 Reorder the terms: -960 + -112t + 16t2 = 960 + -960 + 112t + -112t + -16t2 + 16t2 Combine like terms: 960 + -960 = 0 -960 + -112t + 16t2 = 0 + 112t + -112t + -16t2 + 16t2 -960 + -112t + 16t2 = 112t + -112t + -16t2 + 16t2 Combine like terms: 112t + -112t = 0 -960 + -112t + 16t2 = 0 + -16t2 + 16t2 -960 + -112t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -960 + -112t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-60 + -7t + t2) = 0 Factor a trinomial. 16((-5 + -1t)(12 + -1t)) = 0 Ignore the factor 16.Subproblem 1
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 = -5Subproblem 2
Set the factor '(12 + -1t)' equal to zero and attempt to solve: Simplifying 12 + -1t = 0 Solving 12 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1t = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1t = 0 + -12 -1t = 0 + -12 Combine like terms: 0 + -12 = -12 -1t = -12 Divide each side by '-1'. t = 12 Simplifying t = 12Solution
t = {-5, 12}
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