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Simplifying 5t3 + -9t2 + -2t = 0 Reorder the terms: -2t + -9t2 + 5t3 = 0 Solving -2t + -9t2 + 5t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't'. t(-2 + -9t + 5t2) = 0 Factor a trinomial. t((-1 + -5t)(2 + -1t)) = 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 + -5t)' equal to zero and attempt to solve: Simplifying -1 + -5t = 0 Solving -1 + -5t = 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 + -5t = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5t = 0 + 1 -5t = 0 + 1 Combine like terms: 0 + 1 = 1 -5t = 1 Divide each side by '-5'. t = -0.2 Simplifying t = -0.2Subproblem 3
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 = 2Solution
t = {0, -0.2, 2}
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