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Simplifying t(4t + 6) = 18 Reorder the terms: t(6 + 4t) = 18 (6 * t + 4t * t) = 18 (6t + 4t2) = 18 Solving 6t + 4t2 = 18 Solving for variable 't'. Reorder the terms: -18 + 6t + 4t2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + 6t + 4t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + 3t + 2t2) = 0 Factor a trinomial. 2((-3 + -1t)(3 + -2t)) = 0 Ignore the factor 2.Subproblem 1
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 = -3Subproblem 2
Set the factor '(3 + -2t)' equal to zero and attempt to solve: Simplifying 3 + -2t = 0 Solving 3 + -2t = 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 + -2t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2t = 0 + -3 -2t = 0 + -3 Combine like terms: 0 + -3 = -3 -2t = -3 Divide each side by '-2'. t = 1.5 Simplifying t = 1.5Solution
t = {-3, 1.5}
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