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Simplifying (x + 3)(x + 1) + -1(x + -3)(x + -2) = 3(3x + -1) Reorder the terms: (3 + x)(x + 1) + -1(x + -3)(x + -2) = 3(3x + -1) Reorder the terms: (3 + x)(1 + x) + -1(x + -3)(x + -2) = 3(3x + -1) Multiply (3 + x) * (1 + x) (3(1 + x) + x(1 + x)) + -1(x + -3)(x + -2) = 3(3x + -1) ((1 * 3 + x * 3) + x(1 + x)) + -1(x + -3)(x + -2) = 3(3x + -1) ((3 + 3x) + x(1 + x)) + -1(x + -3)(x + -2) = 3(3x + -1) (3 + 3x + (1 * x + x * x)) + -1(x + -3)(x + -2) = 3(3x + -1) (3 + 3x + (1x + x2)) + -1(x + -3)(x + -2) = 3(3x + -1) Combine like terms: 3x + 1x = 4x (3 + 4x + x2) + -1(x + -3)(x + -2) = 3(3x + -1) Reorder the terms: 3 + 4x + x2 + -1(-3 + x)(x + -2) = 3(3x + -1) Reorder the terms: 3 + 4x + x2 + -1(-3 + x)(-2 + x) = 3(3x + -1) Multiply (-3 + x) * (-2 + x) 3 + 4x + x2 + -1(-3(-2 + x) + x(-2 + x)) = 3(3x + -1) 3 + 4x + x2 + -1((-2 * -3 + x * -3) + x(-2 + x)) = 3(3x + -1) 3 + 4x + x2 + -1((6 + -3x) + x(-2 + x)) = 3(3x + -1) 3 + 4x + x2 + -1(6 + -3x + (-2 * x + x * x)) = 3(3x + -1) 3 + 4x + x2 + -1(6 + -3x + (-2x + x2)) = 3(3x + -1) Combine like terms: -3x + -2x = -5x 3 + 4x + x2 + -1(6 + -5x + x2) = 3(3x + -1) 3 + 4x + x2 + (6 * -1 + -5x * -1 + x2 * -1) = 3(3x + -1) 3 + 4x + x2 + (-6 + 5x + -1x2) = 3(3x + -1) Reorder the terms: 3 + -6 + 4x + 5x + x2 + -1x2 = 3(3x + -1) Combine like terms: 3 + -6 = -3 -3 + 4x + 5x + x2 + -1x2 = 3(3x + -1) Combine like terms: 4x + 5x = 9x -3 + 9x + x2 + -1x2 = 3(3x + -1) Combine like terms: x2 + -1x2 = 0 -3 + 9x + 0 = 3(3x + -1) -3 + 9x = 3(3x + -1) Reorder the terms: -3 + 9x = 3(-1 + 3x) -3 + 9x = (-1 * 3 + 3x * 3) -3 + 9x = (-3 + 9x) Add '3' to each side of the equation. -3 + 3 + 9x = -3 + 3 + 9x Combine like terms: -3 + 3 = 0 0 + 9x = -3 + 3 + 9x 9x = -3 + 3 + 9x Combine like terms: -3 + 3 = 0 9x = 0 + 9x 9x = 9x Add '-9x' to each side of the equation. 9x + -9x = 9x + -9x Combine like terms: 9x + -9x = 0 0 = 9x + -9x Combine like terms: 9x + -9x = 0 0 = 0 Solving 0 = 0 Couldn't find a variable to solve for. This equation is an identity, all real numbers are solutions.
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