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Simplifying t^{2}+ 7t + -35 = 2t + -11 Reorder the terms: -35 + 7t + t^{2}= 2t + -11 Reorder the terms: -35 + 7t + t^{2}= -11 + 2t Solving -35 + 7t + t^{2}= -11 + 2t Solving for variable 't'. Reorder the terms: -35 + 11 + 7t + -2t + t^{2}= -11 + 2t + 11 + -2t Combine like terms: -35 + 11 = -24 -24 + 7t + -2t + t^{2}= -11 + 2t + 11 + -2t Combine like terms: 7t + -2t = 5t -24 + 5t + t^{2}= -11 + 2t + 11 + -2t Reorder the terms: -24 + 5t + t^{2}= -11 + 11 + 2t + -2t Combine like terms: -11 + 11 = 0 -24 + 5t + t^{2}= 0 + 2t + -2t -24 + 5t + t^{2}= 2t + -2t Combine like terms: 2t + -2t = 0 -24 + 5t + t^{2}= 0 Factor a trinomial. (-8 + -1t)(3 + -1t) = 0## Subproblem 1

Set the factor '(-8 + -1t)' equal to zero and attempt to solve: Simplifying -8 + -1t = 0 Solving -8 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1t = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1t = 0 + 8 -1t = 0 + 8 Combine like terms: 0 + 8 = 8 -1t = 8 Divide each side by '-1'. t = -8 Simplifying t = -8## Subproblem 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 = 3## Solution

t = {-8, 3}

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