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Simplifying (5 + 4b)(3x + -6) = (6x + -7)(2b + 10) Reorder the terms: (5 + 4b)(-6 + 3x) = (6x + -7)(2b + 10) Multiply (5 + 4b) * (-6 + 3x) (5(-6 + 3x) + 4b * (-6 + 3x)) = (6x + -7)(2b + 10) ((-6 * 5 + 3x * 5) + 4b * (-6 + 3x)) = (6x + -7)(2b + 10) ((-30 + 15x) + 4b * (-6 + 3x)) = (6x + -7)(2b + 10) (-30 + 15x + (-6 * 4b + 3x * 4b)) = (6x + -7)(2b + 10) (-30 + 15x + (-24b + 12bx)) = (6x + -7)(2b + 10) Reorder the terms: (-30 + -24b + 12bx + 15x) = (6x + -7)(2b + 10) (-30 + -24b + 12bx + 15x) = (6x + -7)(2b + 10) Reorder the terms: -30 + -24b + 12bx + 15x = (-7 + 6x)(2b + 10) Reorder the terms: -30 + -24b + 12bx + 15x = (-7 + 6x)(10 + 2b) Multiply (-7 + 6x) * (10 + 2b) -30 + -24b + 12bx + 15x = (-7(10 + 2b) + 6x * (10 + 2b)) -30 + -24b + 12bx + 15x = ((10 * -7 + 2b * -7) + 6x * (10 + 2b)) -30 + -24b + 12bx + 15x = ((-70 + -14b) + 6x * (10 + 2b)) -30 + -24b + 12bx + 15x = (-70 + -14b + (10 * 6x + 2b * 6x)) Reorder the terms: -30 + -24b + 12bx + 15x = (-70 + -14b + (12bx + 60x)) -30 + -24b + 12bx + 15x = (-70 + -14b + (12bx + 60x)) -30 + -24b + 12bx + 15x = (-70 + -14b + 12bx + 60x) Add '-12bx' to each side of the equation. -30 + -24b + 12bx + -12bx + 15x = -70 + -14b + 12bx + -12bx + 60x Combine like terms: 12bx + -12bx = 0 -30 + -24b + 0 + 15x = -70 + -14b + 12bx + -12bx + 60x -30 + -24b + 15x = -70 + -14b + 12bx + -12bx + 60x Combine like terms: 12bx + -12bx = 0 -30 + -24b + 15x = -70 + -14b + 0 + 60x -30 + -24b + 15x = -70 + -14b + 60x Solving -30 + -24b + 15x = -70 + -14b + 60x Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '14b' to each side of the equation. -30 + -24b + 14b + 15x = -70 + -14b + 14b + 60x Combine like terms: -24b + 14b = -10b -30 + -10b + 15x = -70 + -14b + 14b + 60x Combine like terms: -14b + 14b = 0 -30 + -10b + 15x = -70 + 0 + 60x -30 + -10b + 15x = -70 + 60x Add '30' to each side of the equation. -30 + -10b + 30 + 15x = -70 + 30 + 60x Reorder the terms: -30 + 30 + -10b + 15x = -70 + 30 + 60x Combine like terms: -30 + 30 = 0 0 + -10b + 15x = -70 + 30 + 60x -10b + 15x = -70 + 30 + 60x Combine like terms: -70 + 30 = -40 -10b + 15x = -40 + 60x Add '-15x' to each side of the equation. -10b + 15x + -15x = -40 + 60x + -15x Combine like terms: 15x + -15x = 0 -10b + 0 = -40 + 60x + -15x -10b = -40 + 60x + -15x Combine like terms: 60x + -15x = 45x -10b = -40 + 45x Divide each side by '-10'. b = 4 + -4.5x Simplifying b = 4 + -4.5x
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