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Simplifying 330t + -30t2 = 330 + -30t Solving 330t + -30t2 = 330 + -30t Solving for variable 't'. Reorder the terms: -330 + 330t + 30t + -30t2 = 330 + -30t + -330 + 30t Combine like terms: 330t + 30t = 360t -330 + 360t + -30t2 = 330 + -30t + -330 + 30t Reorder the terms: -330 + 360t + -30t2 = 330 + -330 + -30t + 30t Combine like terms: 330 + -330 = 0 -330 + 360t + -30t2 = 0 + -30t + 30t -330 + 360t + -30t2 = -30t + 30t Combine like terms: -30t + 30t = 0 -330 + 360t + -30t2 = 0 Factor out the Greatest Common Factor (GCF), '30'. 30(-11 + 12t + -1t2) = 0 Factor a trinomial. 30((-11 + t)(1 + -1t)) = 0 Ignore the factor 30.Subproblem 1
Set the factor '(-11 + t)' equal to zero and attempt to solve: Simplifying -11 + t = 0 Solving -11 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + t = 0 + 11 Combine like terms: -11 + 11 = 0 0 + t = 0 + 11 t = 0 + 11 Combine like terms: 0 + 11 = 11 t = 11 Simplifying t = 11Subproblem 2
Set the factor '(1 + -1t)' equal to zero and attempt to solve: Simplifying 1 + -1t = 0 Solving 1 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1t = 0 + -1 -1t = 0 + -1 Combine like terms: 0 + -1 = -1 -1t = -1 Divide each side by '-1'. t = 1 Simplifying t = 1Solution
t = {11, 1}
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