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Simplifying (7t + -9)(2t + 4) + (7t + -9)(3t + 8) = 0 Reorder the terms: (-9 + 7t)(2t + 4) + (7t + -9)(3t + 8) = 0 Reorder the terms: (-9 + 7t)(4 + 2t) + (7t + -9)(3t + 8) = 0 Multiply (-9 + 7t) * (4 + 2t) (-9(4 + 2t) + 7t * (4 + 2t)) + (7t + -9)(3t + 8) = 0 ((4 * -9 + 2t * -9) + 7t * (4 + 2t)) + (7t + -9)(3t + 8) = 0 ((-36 + -18t) + 7t * (4 + 2t)) + (7t + -9)(3t + 8) = 0 (-36 + -18t + (4 * 7t + 2t * 7t)) + (7t + -9)(3t + 8) = 0 (-36 + -18t + (28t + 14t2)) + (7t + -9)(3t + 8) = 0 Combine like terms: -18t + 28t = 10t (-36 + 10t + 14t2) + (7t + -9)(3t + 8) = 0 Reorder the terms: -36 + 10t + 14t2 + (-9 + 7t)(3t + 8) = 0 Reorder the terms: -36 + 10t + 14t2 + (-9 + 7t)(8 + 3t) = 0 Multiply (-9 + 7t) * (8 + 3t) -36 + 10t + 14t2 + (-9(8 + 3t) + 7t * (8 + 3t)) = 0 -36 + 10t + 14t2 + ((8 * -9 + 3t * -9) + 7t * (8 + 3t)) = 0 -36 + 10t + 14t2 + ((-72 + -27t) + 7t * (8 + 3t)) = 0 -36 + 10t + 14t2 + (-72 + -27t + (8 * 7t + 3t * 7t)) = 0 -36 + 10t + 14t2 + (-72 + -27t + (56t + 21t2)) = 0 Combine like terms: -27t + 56t = 29t -36 + 10t + 14t2 + (-72 + 29t + 21t2) = 0 Reorder the terms: -36 + -72 + 10t + 29t + 14t2 + 21t2 = 0 Combine like terms: -36 + -72 = -108 -108 + 10t + 29t + 14t2 + 21t2 = 0 Combine like terms: 10t + 29t = 39t -108 + 39t + 14t2 + 21t2 = 0 Combine like terms: 14t2 + 21t2 = 35t2 -108 + 39t + 35t2 = 0 Solving -108 + 39t + 35t2 = 0 Solving for variable 't'. Factor a trinomial. (-12 + -5t)(9 + -7t) = 0Subproblem 1
Set the factor '(-12 + -5t)' equal to zero and attempt to solve: Simplifying -12 + -5t = 0 Solving -12 + -5t = 0 Move all terms containing t to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -5t = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -5t = 0 + 12 -5t = 0 + 12 Combine like terms: 0 + 12 = 12 -5t = 12 Divide each side by '-5'. t = -2.4 Simplifying t = -2.4Subproblem 2
Set the factor '(9 + -7t)' equal to zero and attempt to solve: Simplifying 9 + -7t = 0 Solving 9 + -7t = 0 Move all terms containing t to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -7t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -7t = 0 + -9 -7t = 0 + -9 Combine like terms: 0 + -9 = -9 -7t = -9 Divide each side by '-7'. t = 1.285714286 Simplifying t = 1.285714286Solution
t = {-2.4, 1.285714286}
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