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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. (-4 + -1t)(5 + -2t) = 0Subproblem 1
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 = -4Subproblem 2
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 = 2.5Solution
t = {-4, 2.5}
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