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Simplifying 2t2 = 216 + 6t Solving 2t2 = 216 + 6t Solving for variable 't'. Reorder the terms: -216 + -6t + 2t2 = 216 + 6t + -216 + -6t Reorder the terms: -216 + -6t + 2t2 = 216 + -216 + 6t + -6t Combine like terms: 216 + -216 = 0 -216 + -6t + 2t2 = 0 + 6t + -6t -216 + -6t + 2t2 = 6t + -6t Combine like terms: 6t + -6t = 0 -216 + -6t + 2t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-108 + -3t + t2) = 0 Factor a trinomial. 2((-9 + -1t)(12 + -1t)) = 0 Ignore the factor 2.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 '(12 + -1t)' equal to zero and attempt to solve: Simplifying 12 + -1t = 0 Solving 12 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1t = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1t = 0 + -12 -1t = 0 + -12 Combine like terms: 0 + -12 = -12 -1t = -12 Divide each side by '-1'. t = 12 Simplifying t = 12Solution
t = {-9, 12}
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