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Simplifying 10t3 + 2t2 + -36t = 0 Reorder the terms: -36t + 2t2 + 10t3 = 0 Solving -36t + 2t2 + 10t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2t'. 2t(-18 + t + 5t2) = 0 Factor a trinomial. 2t((-2 + -1t)(9 + -5t)) = 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 '(-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 '(9 + -5t)' equal to zero and attempt to solve: Simplifying 9 + -5t = 0 Solving 9 + -5t = 0 Move all terms containing t to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -5t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -5t = 0 + -9 -5t = 0 + -9 Combine like terms: 0 + -9 = -9 -5t = -9 Divide each side by '-5'. t = 1.8 Simplifying t = 1.8Solution
t = {0, -2, 1.8}
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