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Simplifying -8 = 2t + -6t2 Solving -8 = 2t + -6t2 Solving for variable 't'. Reorder the terms: -8 + -2t + 6t2 = 2t + -2t + -6t2 + 6t2 Combine like terms: 2t + -2t = 0 -8 + -2t + 6t2 = 0 + -6t2 + 6t2 -8 + -2t + 6t2 = -6t2 + 6t2 Combine like terms: -6t2 + 6t2 = 0 -8 + -2t + 6t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + -1t + 3t2) = 0 Factor a trinomial. 2((-1 + -1t)(4 + -3t)) = 0 Ignore the factor 2.Subproblem 1
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 = -1Subproblem 2
Set the factor '(4 + -3t)' equal to zero and attempt to solve: Simplifying 4 + -3t = 0 Solving 4 + -3t = 0 Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3t = 0 + -4 -3t = 0 + -4 Combine like terms: 0 + -4 = -4 -3t = -4 Divide each side by '-3'. t = 1.333333333 Simplifying t = 1.333333333Solution
t = {-1, 1.333333333}
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