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Simplifying 6t3 + 7t2 + -10t = 0 Reorder the terms: -10t + 7t2 + 6t3 = 0 Solving -10t + 7t2 + 6t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't'. t(-10 + 7t + 6t2) = 0 Factor a trinomial. t((-2 + -1t)(5 + -6t)) = 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 '(-2 + -1t)' equal to zero and attempt to solve: Simplifying -2 + -1t = 0 Solving -2 + -1t = 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 + -1t = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1t = 0 + 2 -1t = 0 + 2 Combine like terms: 0 + 2 = 2 -1t = 2 Divide each side by '-1'. t = -2 Simplifying t = -2Subproblem 3
Set the factor '(5 + -6t)' equal to zero and attempt to solve: Simplifying 5 + -6t = 0 Solving 5 + -6t = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -6t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6t = 0 + -5 -6t = 0 + -5 Combine like terms: 0 + -5 = -5 -6t = -5 Divide each side by '-6'. t = 0.8333333333 Simplifying t = 0.8333333333Solution
t = {0, -2, 0.8333333333}
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