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Simplifying (x + 1)(x + 2)(x + -3) = (x + -2)(x + 1)(x + 1) Reorder the terms: (1 + x)(x + 2)(x + -3) = (x + -2)(x + 1)(x + 1) Reorder the terms: (1 + x)(2 + x)(x + -3) = (x + -2)(x + 1)(x + 1) Reorder the terms: (1 + x)(2 + x)(-3 + x) = (x + -2)(x + 1)(x + 1) Multiply (1 + x) * (2 + x) (1(2 + x) + x(2 + x))(-3 + x) = (x + -2)(x + 1)(x + 1) ((2 * 1 + x * 1) + x(2 + x))(-3 + x) = (x + -2)(x + 1)(x + 1) ((2 + 1x) + x(2 + x))(-3 + x) = (x + -2)(x + 1)(x + 1) (2 + 1x + (2 * x + x * x))(-3 + x) = (x + -2)(x + 1)(x + 1) (2 + 1x + (2x + x2))(-3 + x) = (x + -2)(x + 1)(x + 1) Combine like terms: 1x + 2x = 3x (2 + 3x + x2)(-3 + x) = (x + -2)(x + 1)(x + 1) Multiply (2 + 3x + x2) * (-3 + x) (2(-3 + x) + 3x * (-3 + x) + x2(-3 + x)) = (x + -2)(x + 1)(x + 1) ((-3 * 2 + x * 2) + 3x * (-3 + x) + x2(-3 + x)) = (x + -2)(x + 1)(x + 1) ((-6 + 2x) + 3x * (-3 + x) + x2(-3 + x)) = (x + -2)(x + 1)(x + 1) (-6 + 2x + (-3 * 3x + x * 3x) + x2(-3 + x)) = (x + -2)(x + 1)(x + 1) (-6 + 2x + (-9x + 3x2) + x2(-3 + x)) = (x + -2)(x + 1)(x + 1) (-6 + 2x + -9x + 3x2 + (-3 * x2 + x * x2)) = (x + -2)(x + 1)(x + 1) (-6 + 2x + -9x + 3x2 + (-3x2 + x3)) = (x + -2)(x + 1)(x + 1) Combine like terms: 2x + -9x = -7x (-6 + -7x + 3x2 + -3x2 + x3) = (x + -2)(x + 1)(x + 1) Combine like terms: 3x2 + -3x2 = 0 (-6 + -7x + 0 + x3) = (x + -2)(x + 1)(x + 1) (-6 + -7x + x3) = (x + -2)(x + 1)(x + 1) Reorder the terms: -6 + -7x + x3 = (-2 + x)(x + 1)(x + 1) Reorder the terms: -6 + -7x + x3 = (-2 + x)(1 + x)(x + 1) Reorder the terms: -6 + -7x + x3 = (-2 + x)(1 + x)(1 + x) Multiply (-2 + x) * (1 + x) -6 + -7x + x3 = (-2(1 + x) + x(1 + x))(1 + x) -6 + -7x + x3 = ((1 * -2 + x * -2) + x(1 + x))(1 + x) -6 + -7x + x3 = ((-2 + -2x) + x(1 + x))(1 + x) -6 + -7x + x3 = (-2 + -2x + (1 * x + x * x))(1 + x) -6 + -7x + x3 = (-2 + -2x + (1x + x2))(1 + x) Combine like terms: -2x + 1x = -1x -6 + -7x + x3 = (-2 + -1x + x2)(1 + x) Multiply (-2 + -1x + x2) * (1 + x) -6 + -7x + x3 = (-2(1 + x) + -1x * (1 + x) + x2(1 + x)) -6 + -7x + x3 = ((1 * -2 + x * -2) + -1x * (1 + x) + x2(1 + x)) -6 + -7x + x3 = ((-2 + -2x) + -1x * (1 + x) + x2(1 + x)) -6 + -7x + x3 = (-2 + -2x + (1 * -1x + x * -1x) + x2(1 + x)) -6 + -7x + x3 = (-2 + -2x + (-1x + -1x2) + x2(1 + x)) -6 + -7x + x3 = (-2 + -2x + -1x + -1x2 + (1 * x2 + x * x2)) -6 + -7x + x3 = (-2 + -2x + -1x + -1x2 + (1x2 + x3)) Combine like terms: -2x + -1x = -3x -6 + -7x + x3 = (-2 + -3x + -1x2 + 1x2 + x3) Combine like terms: -1x2 + 1x2 = 0 -6 + -7x + x3 = (-2 + -3x + 0 + x3) -6 + -7x + x3 = (-2 + -3x + x3) Add '-1x3' to each side of the equation. -6 + -7x + x3 + -1x3 = -2 + -3x + x3 + -1x3 Combine like terms: x3 + -1x3 = 0 -6 + -7x + 0 = -2 + -3x + x3 + -1x3 -6 + -7x = -2 + -3x + x3 + -1x3 Combine like terms: x3 + -1x3 = 0 -6 + -7x = -2 + -3x + 0 -6 + -7x = -2 + -3x Solving -6 + -7x = -2 + -3x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3x' to each side of the equation. -6 + -7x + 3x = -2 + -3x + 3x Combine like terms: -7x + 3x = -4x -6 + -4x = -2 + -3x + 3x Combine like terms: -3x + 3x = 0 -6 + -4x = -2 + 0 -6 + -4x = -2 Add '6' to each side of the equation. -6 + 6 + -4x = -2 + 6 Combine like terms: -6 + 6 = 0 0 + -4x = -2 + 6 -4x = -2 + 6 Combine like terms: -2 + 6 = 4 -4x = 4 Divide each side by '-4'. x = -1 Simplifying x = -1
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