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Simplifying 0 = 3t2 + -36t + 81 Reorder the terms: 0 = 81 + -36t + 3t2 Solving 0 = 81 + -36t + 3t2 Solving for variable 't'. Combine like terms: 0 + -81 = -81 -81 + 36t + -3t2 = 81 + -36t + 3t2 + -81 + 36t + -3t2 Reorder the terms: -81 + 36t + -3t2 = 81 + -81 + -36t + 36t + 3t2 + -3t2 Combine like terms: 81 + -81 = 0 -81 + 36t + -3t2 = 0 + -36t + 36t + 3t2 + -3t2 -81 + 36t + -3t2 = -36t + 36t + 3t2 + -3t2 Combine like terms: -36t + 36t = 0 -81 + 36t + -3t2 = 0 + 3t2 + -3t2 -81 + 36t + -3t2 = 3t2 + -3t2 Combine like terms: 3t2 + -3t2 = 0 -81 + 36t + -3t2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-27 + 12t + -1t2) = 0 Factor a trinomial. 3((-9 + t)(3 + -1t)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-9 + t)' equal to zero and attempt to solve: Simplifying -9 + t = 0 Solving -9 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + t = 0 + 9 Combine like terms: -9 + 9 = 0 0 + t = 0 + 9 t = 0 + 9 Combine like terms: 0 + 9 = 9 t = 9 Simplifying t = 9Subproblem 2
Set the factor '(3 + -1t)' equal to zero and attempt to solve: Simplifying 3 + -1t = 0 Solving 3 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1t = 0 + -3 -1t = 0 + -3 Combine like terms: 0 + -3 = -3 -1t = -3 Divide each side by '-1'. t = 3 Simplifying t = 3Solution
t = {9, 3}
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