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Simplifying (2x + 1)(x + 3) = 18 Reorder the terms: (1 + 2x)(x + 3) = 18 Reorder the terms: (1 + 2x)(3 + x) = 18 Multiply (1 + 2x) * (3 + x) (1(3 + x) + 2x * (3 + x)) = 18 ((3 * 1 + x * 1) + 2x * (3 + x)) = 18 ((3 + 1x) + 2x * (3 + x)) = 18 (3 + 1x + (3 * 2x + x * 2x)) = 18 (3 + 1x + (6x + 2x2)) = 18 Combine like terms: 1x + 6x = 7x (3 + 7x + 2x2) = 18 Solving 3 + 7x + 2x2 = 18 Solving for variable 'x'. Reorder the terms: 3 + -18 + 7x + 2x2 = 18 + -18 Combine like terms: 3 + -18 = -15 -15 + 7x + 2x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -15 + 7x + 2x2 = 0 Factor a trinomial. (-5 + -1x)(3 + -2x) = 0Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Solution
x = {-5, 1.5}
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