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Simplifying -12t3 + -13t2 + -3t = 0 Reorder the terms: -3t + -13t2 + -12t3 = 0 Solving -3t + -13t2 + -12t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '-1t'. -1t(3 + 13t + 12t2) = 0 Factor a trinomial. -1t((3 + 4t)(1 + 3t)) = 0 Ignore the factor -1.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 '(3 + 4t)' equal to zero and attempt to solve: Simplifying 3 + 4t = 0 Solving 3 + 4t = 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 + 4t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4t = 0 + -3 4t = 0 + -3 Combine like terms: 0 + -3 = -3 4t = -3 Divide each side by '4'. t = -0.75 Simplifying t = -0.75Subproblem 3
Set the factor '(1 + 3t)' equal to zero and attempt to solve: Simplifying 1 + 3t = 0 Solving 1 + 3t = 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 + 3t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3t = 0 + -1 3t = 0 + -1 Combine like terms: 0 + -1 = -1 3t = -1 Divide each side by '3'. t = -0.3333333333 Simplifying t = -0.3333333333Solution
t = {0, -0.75, -0.3333333333}
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