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Simplifying t(6t + 36) = 330 Reorder the terms: t(36 + 6t) = 330 (36 * t + 6t * t) = 330 (36t + 6t2) = 330 Solving 36t + 6t2 = 330 Solving for variable 't'. Reorder the terms: -330 + 36t + 6t2 = 330 + -330 Combine like terms: 330 + -330 = 0 -330 + 36t + 6t2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-55 + 6t + t2) = 0 Factor a trinomial. 6((-11 + -1t)(5 + -1t)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-11 + -1t)' equal to zero and attempt to solve: Simplifying -11 + -1t = 0 Solving -11 + -1t = 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 + -1t = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -1t = 0 + 11 -1t = 0 + 11 Combine like terms: 0 + 11 = 11 -1t = 11 Divide each side by '-1'. t = -11 Simplifying t = -11Subproblem 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 = {-11, 5}
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