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Simplifying (2t3 + -3t2 + 5t) + -1(6t3 + 3t2 + -5t) = 0 Reorder the terms: (5t + -3t2 + 2t3) + -1(6t3 + 3t2 + -5t) = 0 Remove parenthesis around (5t + -3t2 + 2t3) 5t + -3t2 + 2t3 + -1(6t3 + 3t2 + -5t) = 0 Reorder the terms: 5t + -3t2 + 2t3 + -1(-5t + 3t2 + 6t3) = 0 5t + -3t2 + 2t3 + (-5t * -1 + 3t2 * -1 + 6t3 * -1) = 0 5t + -3t2 + 2t3 + (5t + -3t2 + -6t3) = 0 Reorder the terms: 5t + 5t + -3t2 + -3t2 + 2t3 + -6t3 = 0 Combine like terms: 5t + 5t = 10t 10t + -3t2 + -3t2 + 2t3 + -6t3 = 0 Combine like terms: -3t2 + -3t2 = -6t2 10t + -6t2 + 2t3 + -6t3 = 0 Combine like terms: 2t3 + -6t3 = -4t3 10t + -6t2 + -4t3 = 0 Solving 10t + -6t2 + -4t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2t'. 2t(5 + -3t + -2t2) = 0 Factor a trinomial. 2t((1 + -1t)(5 + 2t)) = 0 Ignore the factor 2.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 '(5 + 2t)' equal to zero and attempt to solve: Simplifying 5 + 2t = 0 Solving 5 + 2t = 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 + 2t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2t = 0 + -5 2t = 0 + -5 Combine like terms: 0 + -5 = -5 2t = -5 Divide each side by '2'. t = -2.5 Simplifying t = -2.5Solution
t = {0, 1, -2.5}
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