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Simplifying 9t3 + 14t2 + -8t = 0 Reorder the terms: -8t + 14t2 + 9t3 = 0 Solving -8t + 14t2 + 9t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't'. t(-8 + 14t + 9t2) = 0 Factor a trinomial. t((-2 + -1t)(4 + -9t)) = 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 '(4 + -9t)' equal to zero and attempt to solve: Simplifying 4 + -9t = 0 Solving 4 + -9t = 0 Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -9t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -9t = 0 + -4 -9t = 0 + -4 Combine like terms: 0 + -4 = -4 -9t = -4 Divide each side by '-9'. t = 0.4444444444 Simplifying t = 0.4444444444Solution
t = {0, -2, 0.4444444444}
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