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Simplifying (3t + 1)(t + -2) = 10 Reorder the terms: (1 + 3t)(t + -2) = 10 Reorder the terms: (1 + 3t)(-2 + t) = 10 Multiply (1 + 3t) * (-2 + t) (1(-2 + t) + 3t * (-2 + t)) = 10 ((-2 * 1 + t * 1) + 3t * (-2 + t)) = 10 ((-2 + 1t) + 3t * (-2 + t)) = 10 (-2 + 1t + (-2 * 3t + t * 3t)) = 10 (-2 + 1t + (-6t + 3t2)) = 10 Combine like terms: 1t + -6t = -5t (-2 + -5t + 3t2) = 10 Solving -2 + -5t + 3t2 = 10 Solving for variable 't'. Reorder the terms: -2 + -10 + -5t + 3t2 = 10 + -10 Combine like terms: -2 + -10 = -12 -12 + -5t + 3t2 = 10 + -10 Combine like terms: 10 + -10 = 0 -12 + -5t + 3t2 = 0 Factor a trinomial. (-4 + -3t)(3 + -1t) = 0Subproblem 1
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 = -1.333333333Subproblem 2
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 = 3Solution
t = {-1.333333333, 3}
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