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Simplifying (10x + 3)(2x + -4) = (5x + -2)(4x + -3) Reorder the terms: (3 + 10x)(2x + -4) = (5x + -2)(4x + -3) Reorder the terms: (3 + 10x)(-4 + 2x) = (5x + -2)(4x + -3) Multiply (3 + 10x) * (-4 + 2x) (3(-4 + 2x) + 10x * (-4 + 2x)) = (5x + -2)(4x + -3) ((-4 * 3 + 2x * 3) + 10x * (-4 + 2x)) = (5x + -2)(4x + -3) ((-12 + 6x) + 10x * (-4 + 2x)) = (5x + -2)(4x + -3) (-12 + 6x + (-4 * 10x + 2x * 10x)) = (5x + -2)(4x + -3) (-12 + 6x + (-40x + 20x2)) = (5x + -2)(4x + -3) Combine like terms: 6x + -40x = -34x (-12 + -34x + 20x2) = (5x + -2)(4x + -3) Reorder the terms: -12 + -34x + 20x2 = (-2 + 5x)(4x + -3) Reorder the terms: -12 + -34x + 20x2 = (-2 + 5x)(-3 + 4x) Multiply (-2 + 5x) * (-3 + 4x) -12 + -34x + 20x2 = (-2(-3 + 4x) + 5x * (-3 + 4x)) -12 + -34x + 20x2 = ((-3 * -2 + 4x * -2) + 5x * (-3 + 4x)) -12 + -34x + 20x2 = ((6 + -8x) + 5x * (-3 + 4x)) -12 + -34x + 20x2 = (6 + -8x + (-3 * 5x + 4x * 5x)) -12 + -34x + 20x2 = (6 + -8x + (-15x + 20x2)) Combine like terms: -8x + -15x = -23x -12 + -34x + 20x2 = (6 + -23x + 20x2) Add '-20x2' to each side of the equation. -12 + -34x + 20x2 + -20x2 = 6 + -23x + 20x2 + -20x2 Combine like terms: 20x2 + -20x2 = 0 -12 + -34x + 0 = 6 + -23x + 20x2 + -20x2 -12 + -34x = 6 + -23x + 20x2 + -20x2 Combine like terms: 20x2 + -20x2 = 0 -12 + -34x = 6 + -23x + 0 -12 + -34x = 6 + -23x Solving -12 + -34x = 6 + -23x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23x' to each side of the equation. -12 + -34x + 23x = 6 + -23x + 23x Combine like terms: -34x + 23x = -11x -12 + -11x = 6 + -23x + 23x Combine like terms: -23x + 23x = 0 -12 + -11x = 6 + 0 -12 + -11x = 6 Add '12' to each side of the equation. -12 + 12 + -11x = 6 + 12 Combine like terms: -12 + 12 = 0 0 + -11x = 6 + 12 -11x = 6 + 12 Combine like terms: 6 + 12 = 18 -11x = 18 Divide each side by '-11'. x = -1.636363636 Simplifying x = -1.636363636
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