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Simplifying (2x + -3)(3x + 2) = (x + -1)(x + 1) + (5x + 2)(x + -4) Reorder the terms: (-3 + 2x)(3x + 2) = (x + -1)(x + 1) + (5x + 2)(x + -4) Reorder the terms: (-3 + 2x)(2 + 3x) = (x + -1)(x + 1) + (5x + 2)(x + -4) Multiply (-3 + 2x) * (2 + 3x) (-3(2 + 3x) + 2x * (2 + 3x)) = (x + -1)(x + 1) + (5x + 2)(x + -4) ((2 * -3 + 3x * -3) + 2x * (2 + 3x)) = (x + -1)(x + 1) + (5x + 2)(x + -4) ((-6 + -9x) + 2x * (2 + 3x)) = (x + -1)(x + 1) + (5x + 2)(x + -4) (-6 + -9x + (2 * 2x + 3x * 2x)) = (x + -1)(x + 1) + (5x + 2)(x + -4) (-6 + -9x + (4x + 6x2)) = (x + -1)(x + 1) + (5x + 2)(x + -4) Combine like terms: -9x + 4x = -5x (-6 + -5x + 6x2) = (x + -1)(x + 1) + (5x + 2)(x + -4) Reorder the terms: -6 + -5x + 6x2 = (-1 + x)(x + 1) + (5x + 2)(x + -4) Reorder the terms: -6 + -5x + 6x2 = (-1 + x)(1 + x) + (5x + 2)(x + -4) Multiply (-1 + x) * (1 + x) -6 + -5x + 6x2 = (-1(1 + x) + x(1 + x)) + (5x + 2)(x + -4) -6 + -5x + 6x2 = ((1 * -1 + x * -1) + x(1 + x)) + (5x + 2)(x + -4) -6 + -5x + 6x2 = ((-1 + -1x) + x(1 + x)) + (5x + 2)(x + -4) -6 + -5x + 6x2 = (-1 + -1x + (1 * x + x * x)) + (5x + 2)(x + -4) -6 + -5x + 6x2 = (-1 + -1x + (1x + x2)) + (5x + 2)(x + -4) Combine like terms: -1x + 1x = 0 -6 + -5x + 6x2 = (-1 + 0 + x2) + (5x + 2)(x + -4) -6 + -5x + 6x2 = (-1 + x2) + (5x + 2)(x + -4) Reorder the terms: -6 + -5x + 6x2 = -1 + x2 + (2 + 5x)(x + -4) Reorder the terms: -6 + -5x + 6x2 = -1 + x2 + (2 + 5x)(-4 + x) Multiply (2 + 5x) * (-4 + x) -6 + -5x + 6x2 = -1 + x2 + (2(-4 + x) + 5x * (-4 + x)) -6 + -5x + 6x2 = -1 + x2 + ((-4 * 2 + x * 2) + 5x * (-4 + x)) -6 + -5x + 6x2 = -1 + x2 + ((-8 + 2x) + 5x * (-4 + x)) -6 + -5x + 6x2 = -1 + x2 + (-8 + 2x + (-4 * 5x + x * 5x)) -6 + -5x + 6x2 = -1 + x2 + (-8 + 2x + (-20x + 5x2)) Combine like terms: 2x + -20x = -18x -6 + -5x + 6x2 = -1 + x2 + (-8 + -18x + 5x2) Reorder the terms: -6 + -5x + 6x2 = -1 + -8 + -18x + x2 + 5x2 Combine like terms: -1 + -8 = -9 -6 + -5x + 6x2 = -9 + -18x + x2 + 5x2 Combine like terms: x2 + 5x2 = 6x2 -6 + -5x + 6x2 = -9 + -18x + 6x2 Add '-6x2' to each side of the equation. -6 + -5x + 6x2 + -6x2 = -9 + -18x + 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -6 + -5x + 0 = -9 + -18x + 6x2 + -6x2 -6 + -5x = -9 + -18x + 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -6 + -5x = -9 + -18x + 0 -6 + -5x = -9 + -18x Solving -6 + -5x = -9 + -18x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18x' to each side of the equation. -6 + -5x + 18x = -9 + -18x + 18x Combine like terms: -5x + 18x = 13x -6 + 13x = -9 + -18x + 18x Combine like terms: -18x + 18x = 0 -6 + 13x = -9 + 0 -6 + 13x = -9 Add '6' to each side of the equation. -6 + 6 + 13x = -9 + 6 Combine like terms: -6 + 6 = 0 0 + 13x = -9 + 6 13x = -9 + 6 Combine like terms: -9 + 6 = -3 13x = -3 Divide each side by '13'. x = -0.2307692308 Simplifying x = -0.2307692308
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