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Simplifying 0 = t2 + -12t + -45 Reorder the terms: 0 = -45 + -12t + t2 Solving 0 = -45 + -12t + t2 Solving for variable 't'. Combine like terms: 0 + 45 = 45 45 + 12t + -1t2 = -45 + -12t + t2 + 45 + 12t + -1t2 Reorder the terms: 45 + 12t + -1t2 = -45 + 45 + -12t + 12t + t2 + -1t2 Combine like terms: -45 + 45 = 0 45 + 12t + -1t2 = 0 + -12t + 12t + t2 + -1t2 45 + 12t + -1t2 = -12t + 12t + t2 + -1t2 Combine like terms: -12t + 12t = 0 45 + 12t + -1t2 = 0 + t2 + -1t2 45 + 12t + -1t2 = t2 + -1t2 Combine like terms: t2 + -1t2 = 0 45 + 12t + -1t2 = 0 Factor a trinomial. (15 + -1t)(3 + t) = 0Subproblem 1
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 = 15Subproblem 2
Set the factor '(3 + t)' equal to zero and attempt to solve: Simplifying 3 + t = 0 Solving 3 + t = 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 + t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + t = 0 + -3 t = 0 + -3 Combine like terms: 0 + -3 = -3 t = -3 Simplifying t = -3Solution
t = {15, -3}
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