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Simplifying (x + -3)(x + 2) + (5 + -1x)(x + 1) = 0 Reorder the terms: (-3 + x)(x + 2) + (5 + -1x)(x + 1) = 0 Reorder the terms: (-3 + x)(2 + x) + (5 + -1x)(x + 1) = 0 Multiply (-3 + x) * (2 + x) (-3(2 + x) + x(2 + x)) + (5 + -1x)(x + 1) = 0 ((2 * -3 + x * -3) + x(2 + x)) + (5 + -1x)(x + 1) = 0 ((-6 + -3x) + x(2 + x)) + (5 + -1x)(x + 1) = 0 (-6 + -3x + (2 * x + x * x)) + (5 + -1x)(x + 1) = 0 (-6 + -3x + (2x + x2)) + (5 + -1x)(x + 1) = 0 Combine like terms: -3x + 2x = -1x (-6 + -1x + x2) + (5 + -1x)(x + 1) = 0 Reorder the terms: -6 + -1x + x2 + (5 + -1x)(1 + x) = 0 Multiply (5 + -1x) * (1 + x) -6 + -1x + x2 + (5(1 + x) + -1x * (1 + x)) = 0 -6 + -1x + x2 + ((1 * 5 + x * 5) + -1x * (1 + x)) = 0 -6 + -1x + x2 + ((5 + 5x) + -1x * (1 + x)) = 0 -6 + -1x + x2 + (5 + 5x + (1 * -1x + x * -1x)) = 0 -6 + -1x + x2 + (5 + 5x + (-1x + -1x2)) = 0 Combine like terms: 5x + -1x = 4x -6 + -1x + x2 + (5 + 4x + -1x2) = 0 Reorder the terms: -6 + 5 + -1x + 4x + x2 + -1x2 = 0 Combine like terms: -6 + 5 = -1 -1 + -1x + 4x + x2 + -1x2 = 0 Combine like terms: -1x + 4x = 3x -1 + 3x + x2 + -1x2 = 0 Combine like terms: x2 + -1x2 = 0 -1 + 3x + 0 = 0 -1 + 3x = 0 Solving -1 + 3x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + 3x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 3x = 0 + 1 3x = 0 + 1 Combine like terms: 0 + 1 = 1 3x = 1 Divide each side by '3'. x = 0.3333333333 Simplifying x = 0.3333333333
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