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Simplifying 12(6t2 + -1t + -2) = 0 Reorder the terms: 12(-2 + -1t + 6t2) = 0 (-2 * 12 + -1t * 12 + 6t2 * 12) = 0 (-24 + -12t + 72t2) = 0 Solving -24 + -12t + 72t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '12'. 12(-2 + -1t + 6t2) = 0 Factor a trinomial. 12((-1 + -2t)(2 + -3t)) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(-1 + -2t)' equal to zero and attempt to solve: Simplifying -1 + -2t = 0 Solving -1 + -2t = 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 + -2t = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2t = 0 + 1 -2t = 0 + 1 Combine like terms: 0 + 1 = 1 -2t = 1 Divide each side by '-2'. t = -0.5 Simplifying t = -0.5Subproblem 2
Set the factor '(2 + -3t)' equal to zero and attempt to solve: Simplifying 2 + -3t = 0 Solving 2 + -3t = 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 + -3t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3t = 0 + -2 -3t = 0 + -2 Combine like terms: 0 + -2 = -2 -3t = -2 Divide each side by '-3'. t = 0.6666666667 Simplifying t = 0.6666666667Solution
t = {-0.5, 0.6666666667}
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