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Simplifying [(2t + -3) * t] * 2 = 40 Reorder the terms: [(-3 + 2t) * t] * 2 = 40 Reorder the terms for easier multiplication: [t(-3 + 2t)] * 2 = 40 [(-3 * t + 2t * t)] * 2 = 40 [(-3t + 2t2)] * 2 = 40 Reorder the terms for easier multiplication: 2[-3t + 2t2] = 40 [-3t * 2 + 2t2 * 2] = 40 [-6t + 4t2] = 40 Solving -6t + 4t2 = 40 Solving for variable 't'. Reorder the terms: -40 + -6t + 4t2 = 40 + -40 Combine like terms: 40 + -40 = 0 -40 + -6t + 4t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-20 + -3t + 2t2) = 0 Factor a trinomial. 2((-5 + -2t)(4 + -1t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -2t)' equal to zero and attempt to solve: Simplifying -5 + -2t = 0 Solving -5 + -2t = 0 Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -2t = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2t = 0 + 5 -2t = 0 + 5 Combine like terms: 0 + 5 = 5 -2t = 5 Divide each side by '-2'. t = -2.5 Simplifying t = -2.5Subproblem 2
Set the factor '(4 + -1t)' equal to zero and attempt to solve: Simplifying 4 + -1t = 0 Solving 4 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1t = 0 + -4 -1t = 0 + -4 Combine like terms: 0 + -4 = -4 -1t = -4 Divide each side by '-1'. t = 4 Simplifying t = 4Solution
t = {-2.5, 4}
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