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Simplifying (5t + -4)(t + 1) = (2t + -9)(t + 1) Reorder the terms: (-4 + 5t)(t + 1) = (2t + -9)(t + 1) Reorder the terms: (-4 + 5t)(1 + t) = (2t + -9)(t + 1) Multiply (-4 + 5t) * (1 + t) (-4(1 + t) + 5t * (1 + t)) = (2t + -9)(t + 1) ((1 * -4 + t * -4) + 5t * (1 + t)) = (2t + -9)(t + 1) ((-4 + -4t) + 5t * (1 + t)) = (2t + -9)(t + 1) (-4 + -4t + (1 * 5t + t * 5t)) = (2t + -9)(t + 1) (-4 + -4t + (5t + 5t2)) = (2t + -9)(t + 1) Combine like terms: -4t + 5t = 1t (-4 + 1t + 5t2) = (2t + -9)(t + 1) Reorder the terms: -4 + 1t + 5t2 = (-9 + 2t)(t + 1) Reorder the terms: -4 + 1t + 5t2 = (-9 + 2t)(1 + t) Multiply (-9 + 2t) * (1 + t) -4 + 1t + 5t2 = (-9(1 + t) + 2t * (1 + t)) -4 + 1t + 5t2 = ((1 * -9 + t * -9) + 2t * (1 + t)) -4 + 1t + 5t2 = ((-9 + -9t) + 2t * (1 + t)) -4 + 1t + 5t2 = (-9 + -9t + (1 * 2t + t * 2t)) -4 + 1t + 5t2 = (-9 + -9t + (2t + 2t2)) Combine like terms: -9t + 2t = -7t -4 + 1t + 5t2 = (-9 + -7t + 2t2) Solving -4 + 1t + 5t2 = -9 + -7t + 2t2 Solving for variable 't'. Reorder the terms: -4 + 9 + 1t + 7t + 5t2 + -2t2 = -9 + -7t + 2t2 + 9 + 7t + -2t2 Combine like terms: -4 + 9 = 5 5 + 1t + 7t + 5t2 + -2t2 = -9 + -7t + 2t2 + 9 + 7t + -2t2 Combine like terms: 1t + 7t = 8t 5 + 8t + 5t2 + -2t2 = -9 + -7t + 2t2 + 9 + 7t + -2t2 Combine like terms: 5t2 + -2t2 = 3t2 5 + 8t + 3t2 = -9 + -7t + 2t2 + 9 + 7t + -2t2 Reorder the terms: 5 + 8t + 3t2 = -9 + 9 + -7t + 7t + 2t2 + -2t2 Combine like terms: -9 + 9 = 0 5 + 8t + 3t2 = 0 + -7t + 7t + 2t2 + -2t2 5 + 8t + 3t2 = -7t + 7t + 2t2 + -2t2 Combine like terms: -7t + 7t = 0 5 + 8t + 3t2 = 0 + 2t2 + -2t2 5 + 8t + 3t2 = 2t2 + -2t2 Combine like terms: 2t2 + -2t2 = 0 5 + 8t + 3t2 = 0 Factor a trinomial. (5 + 3t)(1 + t) = 0Subproblem 1
Set the factor '(5 + 3t)' equal to zero and attempt to solve: Simplifying 5 + 3t = 0 Solving 5 + 3t = 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 + 3t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3t = 0 + -5 3t = 0 + -5 Combine like terms: 0 + -5 = -5 3t = -5 Divide each side by '3'. t = -1.666666667 Simplifying t = -1.666666667Subproblem 2
Set the factor '(1 + t)' equal to zero and attempt to solve: Simplifying 1 + t = 0 Solving 1 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + t = 0 + -1 t = 0 + -1 Combine like terms: 0 + -1 = -1 t = -1 Simplifying t = -1Solution
t = {-1.666666667, -1}
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