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Simplifying 0 = 180 + 3t + -1t2 Solving 0 = 180 + 3t + -1t2 Solving for variable 't'. Combine like terms: 0 + -180 = -180 -180 + -3t + t2 = 180 + 3t + -1t2 + -180 + -3t + t2 Reorder the terms: -180 + -3t + t2 = 180 + -180 + 3t + -3t + -1t2 + t2 Combine like terms: 180 + -180 = 0 -180 + -3t + t2 = 0 + 3t + -3t + -1t2 + t2 -180 + -3t + t2 = 3t + -3t + -1t2 + t2 Combine like terms: 3t + -3t = 0 -180 + -3t + t2 = 0 + -1t2 + t2 -180 + -3t + t2 = -1t2 + t2 Combine like terms: -1t2 + t2 = 0 -180 + -3t + t2 = 0 Factor a trinomial. (-12 + -1t)(15 + -1t) = 0Subproblem 1
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 = -12Subproblem 2
Set the factor '(15 + -1t)' equal to zero and attempt to solve: Simplifying 15 + -1t = 0 Solving 15 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -1t = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1t = 0 + -15 -1t = 0 + -15 Combine like terms: 0 + -15 = -15 -1t = -15 Divide each side by '-1'. t = 15 Simplifying t = 15Solution
t = {-12, 15}
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