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Simplifying (2t3) + (8t2) + -1(24t) = 0 Remove parenthesis around (24t) (2t3) + (8t2) + -1 * 24t = 0 Multiply -1 * 24 (2t3) + (8t2) + -24t = 0 Reorder the terms: -24t + (8t2) + (2t3) = 0 Solving -24t + (8t2) + (2t3) = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2t'. 2t(-12 + (4t) + t2) = 0 Factor a trinomial. 2t((-6 + -1t)(2 + -1t)) = 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 '(-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 = -6Subproblem 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, -6, 2}
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