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Simplifying 2(3t2 + -10) = -7t Reorder the terms: 2(-10 + 3t2) = -7t (-10 * 2 + 3t2 * 2) = -7t (-20 + 6t2) = -7t Solving -20 + 6t2 = -7t Solving for variable 't'. Reorder the terms: -20 + 7t + 6t2 = -7t + 7t Combine like terms: -7t + 7t = 0 -20 + 7t + 6t2 = 0 Factor a trinomial. (-5 + -2t)(4 + -3t) = 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 + -3t)' equal to zero and attempt to solve: Simplifying 4 + -3t = 0 Solving 4 + -3t = 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 + -3t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3t = 0 + -4 -3t = 0 + -4 Combine like terms: 0 + -4 = -4 -3t = -4 Divide each side by '-3'. t = 1.333333333 Simplifying t = 1.333333333Solution
t = {-2.5, 1.333333333}
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