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Simplifying -6t3 = 72t + -42t2 Solving -6t3 = 72t + -42t2 Solving for variable 't'. Reorder the terms: -72t + 42t2 + -6t3 = 72t + -42t2 + -72t + 42t2 Reorder the terms: -72t + 42t2 + -6t3 = 72t + -72t + -42t2 + 42t2 Combine like terms: 72t + -72t = 0 -72t + 42t2 + -6t3 = 0 + -42t2 + 42t2 -72t + 42t2 + -6t3 = -42t2 + 42t2 Combine like terms: -42t2 + 42t2 = 0 -72t + 42t2 + -6t3 = 0 Factor out the Greatest Common Factor (GCF), '6t'. 6t(-12 + 7t + -1t2) = 0 Factor a trinomial. 6t((-4 + t)(3 + -1t)) = 0 Ignore the factor 6.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 '(-4 + t)' equal to zero and attempt to solve: Simplifying -4 + t = 0 Solving -4 + t = 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 + t = 0 + 4 Combine like terms: -4 + 4 = 0 0 + t = 0 + 4 t = 0 + 4 Combine like terms: 0 + 4 = 4 t = 4 Simplifying t = 4Subproblem 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, 4, 3}
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