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Simplifying (2x + 3)(x + 1) = 6 Reorder the terms: (3 + 2x)(x + 1) = 6 Reorder the terms: (3 + 2x)(1 + x) = 6 Multiply (3 + 2x) * (1 + x) (3(1 + x) + 2x * (1 + x)) = 6 ((1 * 3 + x * 3) + 2x * (1 + x)) = 6 ((3 + 3x) + 2x * (1 + x)) = 6 (3 + 3x + (1 * 2x + x * 2x)) = 6 (3 + 3x + (2x + 2x2)) = 6 Combine like terms: 3x + 2x = 5x (3 + 5x + 2x2) = 6 Solving 3 + 5x + 2x2 = 6 Solving for variable 'x'. Reorder the terms: 3 + -6 + 5x + 2x2 = 6 + -6 Combine like terms: 3 + -6 = -3 -3 + 5x + 2x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -3 + 5x + 2x2 = 0 Factor a trinomial. (-3 + -1x)(1 + -2x) = 0Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Solution
x = {-3, 0.5}
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