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Simplifying 8t2 = 12 + 20t Solving 8t2 = 12 + 20t Solving for variable 't'. Reorder the terms: -12 + -20t + 8t2 = 12 + 20t + -12 + -20t Reorder the terms: -12 + -20t + 8t2 = 12 + -12 + 20t + -20t Combine like terms: 12 + -12 = 0 -12 + -20t + 8t2 = 0 + 20t + -20t -12 + -20t + 8t2 = 20t + -20t Combine like terms: 20t + -20t = 0 -12 + -20t + 8t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-3 + -5t + 2t2) = 0 Factor a trinomial. 4((-1 + -2t)(3 + -1t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + -2t)' equal to zero and attempt to solve: Simplifying -1 + -2t = 0 Solving -1 + -2t = 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 + -2t = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2t = 0 + 1 -2t = 0 + 1 Combine like terms: 0 + 1 = 1 -2t = 1 Divide each side by '-2'. t = -0.5 Simplifying t = -0.5Subproblem 2
Set the factor '(3 + -1t)' equal to zero and attempt to solve: Simplifying 3 + -1t = 0 Solving 3 + -1t = 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 + -1t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1t = 0 + -3 -1t = 0 + -3 Combine like terms: 0 + -3 = -3 -1t = -3 Divide each side by '-1'. t = 3 Simplifying t = 3Solution
t = {-0.5, 3}
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