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Simplifying (2x + -1)(3x + 4) = (x + 2)(6x + -5) Reorder the terms: (-1 + 2x)(3x + 4) = (x + 2)(6x + -5) Reorder the terms: (-1 + 2x)(4 + 3x) = (x + 2)(6x + -5) Multiply (-1 + 2x) * (4 + 3x) (-1(4 + 3x) + 2x * (4 + 3x)) = (x + 2)(6x + -5) ((4 * -1 + 3x * -1) + 2x * (4 + 3x)) = (x + 2)(6x + -5) ((-4 + -3x) + 2x * (4 + 3x)) = (x + 2)(6x + -5) (-4 + -3x + (4 * 2x + 3x * 2x)) = (x + 2)(6x + -5) (-4 + -3x + (8x + 6x2)) = (x + 2)(6x + -5) Combine like terms: -3x + 8x = 5x (-4 + 5x + 6x2) = (x + 2)(6x + -5) Reorder the terms: -4 + 5x + 6x2 = (2 + x)(6x + -5) Reorder the terms: -4 + 5x + 6x2 = (2 + x)(-5 + 6x) Multiply (2 + x) * (-5 + 6x) -4 + 5x + 6x2 = (2(-5 + 6x) + x(-5 + 6x)) -4 + 5x + 6x2 = ((-5 * 2 + 6x * 2) + x(-5 + 6x)) -4 + 5x + 6x2 = ((-10 + 12x) + x(-5 + 6x)) -4 + 5x + 6x2 = (-10 + 12x + (-5 * x + 6x * x)) -4 + 5x + 6x2 = (-10 + 12x + (-5x + 6x2)) Combine like terms: 12x + -5x = 7x -4 + 5x + 6x2 = (-10 + 7x + 6x2) Add '-6x2' to each side of the equation. -4 + 5x + 6x2 + -6x2 = -10 + 7x + 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -4 + 5x + 0 = -10 + 7x + 6x2 + -6x2 -4 + 5x = -10 + 7x + 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -4 + 5x = -10 + 7x + 0 -4 + 5x = -10 + 7x Solving -4 + 5x = -10 + 7x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7x' to each side of the equation. -4 + 5x + -7x = -10 + 7x + -7x Combine like terms: 5x + -7x = -2x -4 + -2x = -10 + 7x + -7x Combine like terms: 7x + -7x = 0 -4 + -2x = -10 + 0 -4 + -2x = -10 Add '4' to each side of the equation. -4 + 4 + -2x = -10 + 4 Combine like terms: -4 + 4 = 0 0 + -2x = -10 + 4 -2x = -10 + 4 Combine like terms: -10 + 4 = -6 -2x = -6 Divide each side by '-2'. x = 3 Simplifying x = 3
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