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Simplifying 3t2 + 12t = 135 Reorder the terms: 12t + 3t2 = 135 Solving 12t + 3t2 = 135 Solving for variable 't'. Reorder the terms: -135 + 12t + 3t2 = 135 + -135 Combine like terms: 135 + -135 = 0 -135 + 12t + 3t2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-45 + 4t + t2) = 0 Factor a trinomial. 3((-9 + -1t)(5 + -1t)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-9 + -1t)' equal to zero and attempt to solve: Simplifying -9 + -1t = 0 Solving -9 + -1t = 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 + -1t = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1t = 0 + 9 -1t = 0 + 9 Combine like terms: 0 + 9 = 9 -1t = 9 Divide each side by '-1'. t = -9 Simplifying t = -9Subproblem 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 = {-9, 5}
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