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Simplifying 8t3 + 34t2 + -9t = 0 Reorder the terms: -9t + 34t2 + 8t3 = 0 Solving -9t + 34t2 + 8t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't'. t(-9 + 34t + 8t2) = 0 Factor a trinomial. t((-9 + -2t)(1 + -4t)) = 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 '(-9 + -2t)' equal to zero and attempt to solve: Simplifying -9 + -2t = 0 Solving -9 + -2t = 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 + -2t = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2t = 0 + 9 -2t = 0 + 9 Combine like terms: 0 + 9 = 9 -2t = 9 Divide each side by '-2'. t = -4.5 Simplifying t = -4.5Subproblem 3
Set the factor '(1 + -4t)' equal to zero and attempt to solve: Simplifying 1 + -4t = 0 Solving 1 + -4t = 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 + -4t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4t = 0 + -1 -4t = 0 + -1 Combine like terms: 0 + -1 = -1 -4t = -1 Divide each side by '-4'. t = 0.25 Simplifying t = 0.25Solution
t = {0, -4.5, 0.25}
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