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Simplifying 6t3 = 7t2 + 3t Reorder the terms: 6t3 = 3t + 7t2 Solving 6t3 = 3t + 7t2 Solving for variable 't'. Reorder the terms: -3t + -7t2 + 6t3 = 3t + 7t2 + -3t + -7t2 Reorder the terms: -3t + -7t2 + 6t3 = 3t + -3t + 7t2 + -7t2 Combine like terms: 3t + -3t = 0 -3t + -7t2 + 6t3 = 0 + 7t2 + -7t2 -3t + -7t2 + 6t3 = 7t2 + -7t2 Combine like terms: 7t2 + -7t2 = 0 -3t + -7t2 + 6t3 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-3 + -7t + 6t2) = 0 Factor a trinomial. t((-1 + -3t)(3 + -2t)) = 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 + -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 = -0.3333333333Subproblem 3
Set the factor '(3 + -2t)' equal to zero and attempt to solve: Simplifying 3 + -2t = 0 Solving 3 + -2t = 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 + -2t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2t = 0 + -3 -2t = 0 + -3 Combine like terms: 0 + -3 = -3 -2t = -3 Divide each side by '-2'. t = 1.5 Simplifying t = 1.5Solution
t = {0, -0.3333333333, 1.5}
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