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Simplifying (9t + -8)(3t + 4) + (9t + -8)(7t + 5) = 0 Reorder the terms: (-8 + 9t)(3t + 4) + (9t + -8)(7t + 5) = 0 Reorder the terms: (-8 + 9t)(4 + 3t) + (9t + -8)(7t + 5) = 0 Multiply (-8 + 9t) * (4 + 3t) (-8(4 + 3t) + 9t * (4 + 3t)) + (9t + -8)(7t + 5) = 0 ((4 * -8 + 3t * -8) + 9t * (4 + 3t)) + (9t + -8)(7t + 5) = 0 ((-32 + -24t) + 9t * (4 + 3t)) + (9t + -8)(7t + 5) = 0 (-32 + -24t + (4 * 9t + 3t * 9t)) + (9t + -8)(7t + 5) = 0 (-32 + -24t + (36t + 27t2)) + (9t + -8)(7t + 5) = 0 Combine like terms: -24t + 36t = 12t (-32 + 12t + 27t2) + (9t + -8)(7t + 5) = 0 Reorder the terms: -32 + 12t + 27t2 + (-8 + 9t)(7t + 5) = 0 Reorder the terms: -32 + 12t + 27t2 + (-8 + 9t)(5 + 7t) = 0 Multiply (-8 + 9t) * (5 + 7t) -32 + 12t + 27t2 + (-8(5 + 7t) + 9t * (5 + 7t)) = 0 -32 + 12t + 27t2 + ((5 * -8 + 7t * -8) + 9t * (5 + 7t)) = 0 -32 + 12t + 27t2 + ((-40 + -56t) + 9t * (5 + 7t)) = 0 -32 + 12t + 27t2 + (-40 + -56t + (5 * 9t + 7t * 9t)) = 0 -32 + 12t + 27t2 + (-40 + -56t + (45t + 63t2)) = 0 Combine like terms: -56t + 45t = -11t -32 + 12t + 27t2 + (-40 + -11t + 63t2) = 0 Reorder the terms: -32 + -40 + 12t + -11t + 27t2 + 63t2 = 0 Combine like terms: -32 + -40 = -72 -72 + 12t + -11t + 27t2 + 63t2 = 0 Combine like terms: 12t + -11t = 1t -72 + 1t + 27t2 + 63t2 = 0 Combine like terms: 27t2 + 63t2 = 90t2 -72 + 1t + 90t2 = 0 Solving -72 + 1t + 90t2 = 0 Solving for variable 't'. Factor a trinomial. (-9 + -10t)(8 + -9t) = 0Subproblem 1
Set the factor '(-9 + -10t)' equal to zero and attempt to solve: Simplifying -9 + -10t = 0 Solving -9 + -10t = 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 + -10t = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -10t = 0 + 9 -10t = 0 + 9 Combine like terms: 0 + 9 = 9 -10t = 9 Divide each side by '-10'. t = -0.9 Simplifying t = -0.9Subproblem 2
Set the factor '(8 + -9t)' equal to zero and attempt to solve: Simplifying 8 + -9t = 0 Solving 8 + -9t = 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 + -9t = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -9t = 0 + -8 -9t = 0 + -8 Combine like terms: 0 + -8 = -8 -9t = -8 Divide each side by '-9'. t = 0.8888888889 Simplifying t = 0.8888888889Solution
t = {-0.9, 0.8888888889}
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