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Simplifying -2t3 = 60t + -26t2 Solving -2t3 = 60t + -26t2 Solving for variable 't'. Reorder the terms: -60t + 26t2 + -2t3 = 60t + -26t2 + -60t + 26t2 Reorder the terms: -60t + 26t2 + -2t3 = 60t + -60t + -26t2 + 26t2 Combine like terms: 60t + -60t = 0 -60t + 26t2 + -2t3 = 0 + -26t2 + 26t2 -60t + 26t2 + -2t3 = -26t2 + 26t2 Combine like terms: -26t2 + 26t2 = 0 -60t + 26t2 + -2t3 = 0 Factor out the Greatest Common Factor (GCF), '2t'. 2t(-30 + 13t + -1t2) = 0 Factor a trinomial. 2t((-10 + t)(3 + -1t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0Subproblem 2
Set the factor '(-10 + t)' equal to zero and attempt to solve: Simplifying -10 + t = 0 Solving -10 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + t = 0 + 10 Combine like terms: -10 + 10 = 0 0 + t = 0 + 10 t = 0 + 10 Combine like terms: 0 + 10 = 10 t = 10 Simplifying t = 10Subproblem 3
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, 10, 3}
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