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Simplifying (3x + -2)(2x + 1) = (3x + -1)(2x + 3) Reorder the terms: (-2 + 3x)(2x + 1) = (3x + -1)(2x + 3) Reorder the terms: (-2 + 3x)(1 + 2x) = (3x + -1)(2x + 3) Multiply (-2 + 3x) * (1 + 2x) (-2(1 + 2x) + 3x * (1 + 2x)) = (3x + -1)(2x + 3) ((1 * -2 + 2x * -2) + 3x * (1 + 2x)) = (3x + -1)(2x + 3) ((-2 + -4x) + 3x * (1 + 2x)) = (3x + -1)(2x + 3) (-2 + -4x + (1 * 3x + 2x * 3x)) = (3x + -1)(2x + 3) (-2 + -4x + (3x + 6x2)) = (3x + -1)(2x + 3) Combine like terms: -4x + 3x = -1x (-2 + -1x + 6x2) = (3x + -1)(2x + 3) Reorder the terms: -2 + -1x + 6x2 = (-1 + 3x)(2x + 3) Reorder the terms: -2 + -1x + 6x2 = (-1 + 3x)(3 + 2x) Multiply (-1 + 3x) * (3 + 2x) -2 + -1x + 6x2 = (-1(3 + 2x) + 3x * (3 + 2x)) -2 + -1x + 6x2 = ((3 * -1 + 2x * -1) + 3x * (3 + 2x)) -2 + -1x + 6x2 = ((-3 + -2x) + 3x * (3 + 2x)) -2 + -1x + 6x2 = (-3 + -2x + (3 * 3x + 2x * 3x)) -2 + -1x + 6x2 = (-3 + -2x + (9x + 6x2)) Combine like terms: -2x + 9x = 7x -2 + -1x + 6x2 = (-3 + 7x + 6x2) Add '-6x2' to each side of the equation. -2 + -1x + 6x2 + -6x2 = -3 + 7x + 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -2 + -1x + 0 = -3 + 7x + 6x2 + -6x2 -2 + -1x = -3 + 7x + 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -2 + -1x = -3 + 7x + 0 -2 + -1x = -3 + 7x Solving -2 + -1x = -3 + 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. -2 + -1x + -7x = -3 + 7x + -7x Combine like terms: -1x + -7x = -8x -2 + -8x = -3 + 7x + -7x Combine like terms: 7x + -7x = 0 -2 + -8x = -3 + 0 -2 + -8x = -3 Add '2' to each side of the equation. -2 + 2 + -8x = -3 + 2 Combine like terms: -2 + 2 = 0 0 + -8x = -3 + 2 -8x = -3 + 2 Combine like terms: -3 + 2 = -1 -8x = -1 Divide each side by '-8'. x = 0.125 Simplifying x = 0.125
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