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Simplifying (x + 1)(x + 2) = 6 Reorder the terms: (1 + x)(x + 2) = 6 Reorder the terms: (1 + x)(2 + x) = 6 Multiply (1 + x) * (2 + x) (1(2 + x) + x(2 + x)) = 6 ((2 * 1 + x * 1) + x(2 + x)) = 6 ((2 + 1x) + x(2 + x)) = 6 (2 + 1x + (2 * x + x * x)) = 6 (2 + 1x + (2x + x2)) = 6 Combine like terms: 1x + 2x = 3x (2 + 3x + x2) = 6 Solving 2 + 3x + x2 = 6 Solving for variable 'x'. Reorder the terms: 2 + -6 + 3x + x2 = 6 + -6 Combine like terms: 2 + -6 = -4 -4 + 3x + x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -4 + 3x + x2 = 0 Factor a trinomial. (-4 + -1x)(1 + -1x) = 0Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {-4, 1}
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