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Simplifying (x + 3)(x + -4) = (x + -2)(x + -1) Reorder the terms: (3 + x)(x + -4) = (x + -2)(x + -1) Reorder the terms: (3 + x)(-4 + x) = (x + -2)(x + -1) Multiply (3 + x) * (-4 + x) (3(-4 + x) + x(-4 + x)) = (x + -2)(x + -1) ((-4 * 3 + x * 3) + x(-4 + x)) = (x + -2)(x + -1) ((-12 + 3x) + x(-4 + x)) = (x + -2)(x + -1) (-12 + 3x + (-4 * x + x * x)) = (x + -2)(x + -1) (-12 + 3x + (-4x + x2)) = (x + -2)(x + -1) Combine like terms: 3x + -4x = -1x (-12 + -1x + x2) = (x + -2)(x + -1) Reorder the terms: -12 + -1x + x2 = (-2 + x)(x + -1) Reorder the terms: -12 + -1x + x2 = (-2 + x)(-1 + x) Multiply (-2 + x) * (-1 + x) -12 + -1x + x2 = (-2(-1 + x) + x(-1 + x)) -12 + -1x + x2 = ((-1 * -2 + x * -2) + x(-1 + x)) -12 + -1x + x2 = ((2 + -2x) + x(-1 + x)) -12 + -1x + x2 = (2 + -2x + (-1 * x + x * x)) -12 + -1x + x2 = (2 + -2x + (-1x + x2)) Combine like terms: -2x + -1x = -3x -12 + -1x + x2 = (2 + -3x + x2) Add '-1x2' to each side of the equation. -12 + -1x + x2 + -1x2 = 2 + -3x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -12 + -1x + 0 = 2 + -3x + x2 + -1x2 -12 + -1x = 2 + -3x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -12 + -1x = 2 + -3x + 0 -12 + -1x = 2 + -3x Solving -12 + -1x = 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. -12 + -1x + 3x = 2 + -3x + 3x Combine like terms: -1x + 3x = 2x -12 + 2x = 2 + -3x + 3x Combine like terms: -3x + 3x = 0 -12 + 2x = 2 + 0 -12 + 2x = 2 Add '12' to each side of the equation. -12 + 12 + 2x = 2 + 12 Combine like terms: -12 + 12 = 0 0 + 2x = 2 + 12 2x = 2 + 12 Combine like terms: 2 + 12 = 14 2x = 14 Divide each side by '2'. x = 7 Simplifying x = 7
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