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