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Simplifying (2t + 3)(9t + -7) = (6t + 5)(3t + -4) Reorder the terms: (3 + 2t)(9t + -7) = (6t + 5)(3t + -4) Reorder the terms: (3 + 2t)(-7 + 9t) = (6t + 5)(3t + -4) Multiply (3 + 2t) * (-7 + 9t) (3(-7 + 9t) + 2t * (-7 + 9t)) = (6t + 5)(3t + -4) ((-7 * 3 + 9t * 3) + 2t * (-7 + 9t)) = (6t + 5)(3t + -4) ((-21 + 27t) + 2t * (-7 + 9t)) = (6t + 5)(3t + -4) (-21 + 27t + (-7 * 2t + 9t * 2t)) = (6t + 5)(3t + -4) (-21 + 27t + (-14t + 18t2)) = (6t + 5)(3t + -4) Combine like terms: 27t + -14t = 13t (-21 + 13t + 18t2) = (6t + 5)(3t + -4) Reorder the terms: -21 + 13t + 18t2 = (5 + 6t)(3t + -4) Reorder the terms: -21 + 13t + 18t2 = (5 + 6t)(-4 + 3t) Multiply (5 + 6t) * (-4 + 3t) -21 + 13t + 18t2 = (5(-4 + 3t) + 6t * (-4 + 3t)) -21 + 13t + 18t2 = ((-4 * 5 + 3t * 5) + 6t * (-4 + 3t)) -21 + 13t + 18t2 = ((-20 + 15t) + 6t * (-4 + 3t)) -21 + 13t + 18t2 = (-20 + 15t + (-4 * 6t + 3t * 6t)) -21 + 13t + 18t2 = (-20 + 15t + (-24t + 18t2)) Combine like terms: 15t + -24t = -9t -21 + 13t + 18t2 = (-20 + -9t + 18t2) Add '-18t2' to each side of the equation. -21 + 13t + 18t2 + -18t2 = -20 + -9t + 18t2 + -18t2 Combine like terms: 18t2 + -18t2 = 0 -21 + 13t + 0 = -20 + -9t + 18t2 + -18t2 -21 + 13t = -20 + -9t + 18t2 + -18t2 Combine like terms: 18t2 + -18t2 = 0 -21 + 13t = -20 + -9t + 0 -21 + 13t = -20 + -9t Solving -21 + 13t = -20 + -9t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9t' to each side of the equation. -21 + 13t + 9t = -20 + -9t + 9t Combine like terms: 13t + 9t = 22t -21 + 22t = -20 + -9t + 9t Combine like terms: -9t + 9t = 0 -21 + 22t = -20 + 0 -21 + 22t = -20 Add '21' to each side of the equation. -21 + 21 + 22t = -20 + 21 Combine like terms: -21 + 21 = 0 0 + 22t = -20 + 21 22t = -20 + 21 Combine like terms: -20 + 21 = 1 22t = 1 Divide each side by '22'. t = 0.04545454545 Simplifying t = 0.04545454545
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