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Simplifying t(2t + -3) = 20 Reorder the terms: t(-3 + 2t) = 20 (-3 * t + 2t * t) = 20 (-3t + 2t2) = 20 Solving -3t + 2t2 = 20 Solving for variable 't'. Reorder the terms: -20 + -3t + 2t2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + -3t + 2t2 = 0 Factor a trinomial. (-5 + -2t)(4 + -1t) = 0Subproblem 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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