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Simplifying t3 + 8t2 + -84t = 0 Reorder the terms: -84t + 8t2 + t3 = 0 Solving -84t + 8t2 + t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't'. t(-84 + 8t + t2) = 0 Factor a trinomial. t((-14 + -1t)(6 + -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 '(-14 + -1t)' equal to zero and attempt to solve: Simplifying -14 + -1t = 0 Solving -14 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + -1t = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -1t = 0 + 14 -1t = 0 + 14 Combine like terms: 0 + 14 = 14 -1t = 14 Divide each side by '-1'. t = -14 Simplifying t = -14Subproblem 3
Set the factor '(6 + -1t)' equal to zero and attempt to solve: Simplifying 6 + -1t = 0 Solving 6 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1t = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1t = 0 + -6 -1t = 0 + -6 Combine like terms: 0 + -6 = -6 -1t = -6 Divide each side by '-1'. t = 6 Simplifying t = 6Solution
t = {0, -14, 6}
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