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Simplifying -6t = t2 + -1t3 Solving -6t = t2 + -1t3 Solving for variable 't'. Reorder the terms: -6t + -1t2 + t3 = t2 + -1t2 + -1t3 + t3 Combine like terms: t2 + -1t2 = 0 -6t + -1t2 + t3 = 0 + -1t3 + t3 -6t + -1t2 + t3 = -1t3 + t3 Combine like terms: -1t3 + t3 = 0 -6t + -1t2 + t3 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-6 + -1t + t2) = 0 Factor a trinomial. t((-2 + -1t)(3 + -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 '(-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 '(3 + -1t)' equal to zero and attempt to solve: Simplifying 3 + -1t = 0 Solving 3 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1t = 0 + -3 -1t = 0 + -3 Combine like terms: 0 + -3 = -3 -1t = -3 Divide each side by '-1'. t = 3 Simplifying t = 3Solution
t = {0, -2, 3}
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