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Simplifying t3 + 5t2 + -6t = 0 Reorder the terms: -6t + 5t2 + t3 = 0 Solving -6t + 5t2 + t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't'. t(-6 + 5t + t2) = 0 Factor a trinomial. t((-6 + -1t)(1 + -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 '(-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 '(1 + -1t)' equal to zero and attempt to solve: Simplifying 1 + -1t = 0 Solving 1 + -1t = 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 + -1t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1t = 0 + -1 -1t = 0 + -1 Combine like terms: 0 + -1 = -1 -1t = -1 Divide each side by '-1'. t = 1 Simplifying t = 1Solution
t = {0, -6, 1}
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