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Simplifying (2x + 3)(2x + -1) = (x + -2)(4x + 3) Reorder the terms: (3 + 2x)(2x + -1) = (x + -2)(4x + 3) Reorder the terms: (3 + 2x)(-1 + 2x) = (x + -2)(4x + 3) Multiply (3 + 2x) * (-1 + 2x) (3(-1 + 2x) + 2x * (-1 + 2x)) = (x + -2)(4x + 3) ((-1 * 3 + 2x * 3) + 2x * (-1 + 2x)) = (x + -2)(4x + 3) ((-3 + 6x) + 2x * (-1 + 2x)) = (x + -2)(4x + 3) (-3 + 6x + (-1 * 2x + 2x * 2x)) = (x + -2)(4x + 3) (-3 + 6x + (-2x + 4x2)) = (x + -2)(4x + 3) Combine like terms: 6x + -2x = 4x (-3 + 4x + 4x2) = (x + -2)(4x + 3) Reorder the terms: -3 + 4x + 4x2 = (-2 + x)(4x + 3) Reorder the terms: -3 + 4x + 4x2 = (-2 + x)(3 + 4x) Multiply (-2 + x) * (3 + 4x) -3 + 4x + 4x2 = (-2(3 + 4x) + x(3 + 4x)) -3 + 4x + 4x2 = ((3 * -2 + 4x * -2) + x(3 + 4x)) -3 + 4x + 4x2 = ((-6 + -8x) + x(3 + 4x)) -3 + 4x + 4x2 = (-6 + -8x + (3 * x + 4x * x)) -3 + 4x + 4x2 = (-6 + -8x + (3x + 4x2)) Combine like terms: -8x + 3x = -5x -3 + 4x + 4x2 = (-6 + -5x + 4x2) Add '-4x2' to each side of the equation. -3 + 4x + 4x2 + -4x2 = -6 + -5x + 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -3 + 4x + 0 = -6 + -5x + 4x2 + -4x2 -3 + 4x = -6 + -5x + 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -3 + 4x = -6 + -5x + 0 -3 + 4x = -6 + -5x Solving -3 + 4x = -6 + -5x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5x' to each side of the equation. -3 + 4x + 5x = -6 + -5x + 5x Combine like terms: 4x + 5x = 9x -3 + 9x = -6 + -5x + 5x Combine like terms: -5x + 5x = 0 -3 + 9x = -6 + 0 -3 + 9x = -6 Add '3' to each side of the equation. -3 + 3 + 9x = -6 + 3 Combine like terms: -3 + 3 = 0 0 + 9x = -6 + 3 9x = -6 + 3 Combine like terms: -6 + 3 = -3 9x = -3 Divide each side by '9'. x = -0.3333333333 Simplifying x = -0.3333333333
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