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Simplifying (x + 4)(2x + 3) = -3 Reorder the terms: (4 + x)(2x + 3) = -3 Reorder the terms: (4 + x)(3 + 2x) = -3 Multiply (4 + x) * (3 + 2x) (4(3 + 2x) + x(3 + 2x)) = -3 ((3 * 4 + 2x * 4) + x(3 + 2x)) = -3 ((12 + 8x) + x(3 + 2x)) = -3 (12 + 8x + (3 * x + 2x * x)) = -3 (12 + 8x + (3x + 2x2)) = -3 Combine like terms: 8x + 3x = 11x (12 + 11x + 2x2) = -3 Solving 12 + 11x + 2x2 = -3 Solving for variable 'x'. Reorder the terms: 12 + 3 + 11x + 2x2 = -3 + 3 Combine like terms: 12 + 3 = 15 15 + 11x + 2x2 = -3 + 3 Combine like terms: -3 + 3 = 0 15 + 11x + 2x2 = 0 Factor a trinomial. (3 + x)(5 + 2x) = 0Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Subproblem 2
Set the factor '(5 + 2x)' equal to zero and attempt to solve: Simplifying 5 + 2x = 0 Solving 5 + 2x = 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 + 2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2x = 0 + -5 2x = 0 + -5 Combine like terms: 0 + -5 = -5 2x = -5 Divide each side by '2'. x = -2.5 Simplifying x = -2.5Solution
x = {-3, -2.5}
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