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Simplifying -16t2 + 192t + -560 = 0 Reorder the terms: -560 + 192t + -16t2 = 0 Solving -560 + 192t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '16'. 16(-35 + 12t + -1t2) = 0 Factor a trinomial. 16((-7 + t)(5 + -1t)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-7 + t)' equal to zero and attempt to solve: Simplifying -7 + t = 0 Solving -7 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + t = 0 + 7 Combine like terms: -7 + 7 = 0 0 + t = 0 + 7 t = 0 + 7 Combine like terms: 0 + 7 = 7 t = 7 Simplifying t = 7Subproblem 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 = {7, 5}
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