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Simplifying 12t3 + -19t2 + 4t = 0 Reorder the terms: 4t + -19t2 + 12t3 = 0 Solving 4t + -19t2 + 12t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't'. t(4 + -19t + 12t2) = 0 Factor a trinomial. t((1 + -4t)(4 + -3t)) = 0Subproblem 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 + -4t)' equal to zero and attempt to solve: Simplifying 1 + -4t = 0 Solving 1 + -4t = 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 + -4t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4t = 0 + -1 -4t = 0 + -1 Combine like terms: 0 + -1 = -1 -4t = -1 Divide each side by '-4'. t = 0.25 Simplifying t = 0.25Subproblem 3
Set the factor '(4 + -3t)' equal to zero and attempt to solve: Simplifying 4 + -3t = 0 Solving 4 + -3t = 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 + -3t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3t = 0 + -4 -3t = 0 + -4 Combine like terms: 0 + -4 = -4 -3t = -4 Divide each side by '-3'. t = 1.333333333 Simplifying t = 1.333333333Solution
t = {0, 0.25, 1.333333333}
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