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Simplifying 12t2 = 40 + 52t Solving 12t2 = 40 + 52t Solving for variable 't'. Reorder the terms: -40 + -52t + 12t2 = 40 + 52t + -40 + -52t Reorder the terms: -40 + -52t + 12t2 = 40 + -40 + 52t + -52t Combine like terms: 40 + -40 = 0 -40 + -52t + 12t2 = 0 + 52t + -52t -40 + -52t + 12t2 = 52t + -52t Combine like terms: 52t + -52t = 0 -40 + -52t + 12t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-10 + -13t + 3t2) = 0 Factor a trinomial. 4((-2 + -3t)(5 + -1t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-2 + -3t)' equal to zero and attempt to solve: Simplifying -2 + -3t = 0 Solving -2 + -3t = 0 Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -3t = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3t = 0 + 2 -3t = 0 + 2 Combine like terms: 0 + 2 = 2 -3t = 2 Divide each side by '-3'. t = -0.6666666667 Simplifying t = -0.6666666667Subproblem 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 = {-0.6666666667, 5}
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