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Simplifying (6x + 5)(3x + -4) = (2x + 3)(9x + -7) Reorder the terms: (5 + 6x)(3x + -4) = (2x + 3)(9x + -7) Reorder the terms: (5 + 6x)(-4 + 3x) = (2x + 3)(9x + -7) Multiply (5 + 6x) * (-4 + 3x) (5(-4 + 3x) + 6x * (-4 + 3x)) = (2x + 3)(9x + -7) ((-4 * 5 + 3x * 5) + 6x * (-4 + 3x)) = (2x + 3)(9x + -7) ((-20 + 15x) + 6x * (-4 + 3x)) = (2x + 3)(9x + -7) (-20 + 15x + (-4 * 6x + 3x * 6x)) = (2x + 3)(9x + -7) (-20 + 15x + (-24x + 18x2)) = (2x + 3)(9x + -7) Combine like terms: 15x + -24x = -9x (-20 + -9x + 18x2) = (2x + 3)(9x + -7) Reorder the terms: -20 + -9x + 18x2 = (3 + 2x)(9x + -7) Reorder the terms: -20 + -9x + 18x2 = (3 + 2x)(-7 + 9x) Multiply (3 + 2x) * (-7 + 9x) -20 + -9x + 18x2 = (3(-7 + 9x) + 2x * (-7 + 9x)) -20 + -9x + 18x2 = ((-7 * 3 + 9x * 3) + 2x * (-7 + 9x)) -20 + -9x + 18x2 = ((-21 + 27x) + 2x * (-7 + 9x)) -20 + -9x + 18x2 = (-21 + 27x + (-7 * 2x + 9x * 2x)) -20 + -9x + 18x2 = (-21 + 27x + (-14x + 18x2)) Combine like terms: 27x + -14x = 13x -20 + -9x + 18x2 = (-21 + 13x + 18x2) Add '-18x2' to each side of the equation. -20 + -9x + 18x2 + -18x2 = -21 + 13x + 18x2 + -18x2 Combine like terms: 18x2 + -18x2 = 0 -20 + -9x + 0 = -21 + 13x + 18x2 + -18x2 -20 + -9x = -21 + 13x + 18x2 + -18x2 Combine like terms: 18x2 + -18x2 = 0 -20 + -9x = -21 + 13x + 0 -20 + -9x = -21 + 13x Solving -20 + -9x = -21 + 13x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13x' to each side of the equation. -20 + -9x + -13x = -21 + 13x + -13x Combine like terms: -9x + -13x = -22x -20 + -22x = -21 + 13x + -13x Combine like terms: 13x + -13x = 0 -20 + -22x = -21 + 0 -20 + -22x = -21 Add '20' to each side of the equation. -20 + 20 + -22x = -21 + 20 Combine like terms: -20 + 20 = 0 0 + -22x = -21 + 20 -22x = -21 + 20 Combine like terms: -21 + 20 = -1 -22x = -1 Divide each side by '-22'. x = 0.04545454545 Simplifying x = 0.04545454545
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