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