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