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Simplifying 6t2 = 34t + -20 Reorder the terms: 6t2 = -20 + 34t Solving 6t2 = -20 + 34t Solving for variable 't'. Reorder the terms: 20 + -34t + 6t2 = -20 + 34t + 20 + -34t Reorder the terms: 20 + -34t + 6t2 = -20 + 20 + 34t + -34t Combine like terms: -20 + 20 = 0 20 + -34t + 6t2 = 0 + 34t + -34t 20 + -34t + 6t2 = 34t + -34t Combine like terms: 34t + -34t = 0 20 + -34t + 6t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(10 + -17t + 3t2) = 0 Factor a trinomial. 2((2 + -3t)(5 + -1t)) = 0 Ignore the factor 2.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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