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Simplifying 12t = 6t3 + 6t2 Reorder the terms: 12t = 6t2 + 6t3 Solving 12t = 6t2 + 6t3 Solving for variable 't'. Reorder the terms: 12t + -6t2 + -6t3 = 6t2 + -6t2 + 6t3 + -6t3 Combine like terms: 6t2 + -6t2 = 0 12t + -6t2 + -6t3 = 0 + 6t3 + -6t3 12t + -6t2 + -6t3 = 6t3 + -6t3 Combine like terms: 6t3 + -6t3 = 0 12t + -6t2 + -6t3 = 0 Factor out the Greatest Common Factor (GCF), '6t'. 6t(2 + -1t + -1t2) = 0 Factor a trinomial. 6t((1 + -1t)(2 + t)) = 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 '(1 + -1t)' equal to zero and attempt to solve: Simplifying 1 + -1t = 0 Solving 1 + -1t = 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 + -1t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1t = 0 + -1 -1t = 0 + -1 Combine like terms: 0 + -1 = -1 -1t = -1 Divide each side by '-1'. t = 1 Simplifying t = 1Subproblem 3
Set the factor '(2 + t)' equal to zero and attempt to solve: Simplifying 2 + t = 0 Solving 2 + t = 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 + t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + t = 0 + -2 t = 0 + -2 Combine like terms: 0 + -2 = -2 t = -2 Simplifying t = -2Solution
t = {0, 1, -2}
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