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Simplifying (2x + 3)(x + 4) = 0 Reorder the terms: (3 + 2x)(x + 4) = 0 Reorder the terms: (3 + 2x)(4 + x) = 0 Multiply (3 + 2x) * (4 + x) (3(4 + x) + 2x * (4 + x)) = 0 ((4 * 3 + x * 3) + 2x * (4 + x)) = 0 ((12 + 3x) + 2x * (4 + x)) = 0 (12 + 3x + (4 * 2x + x * 2x)) = 0 (12 + 3x + (8x + 2x2)) = 0 Combine like terms: 3x + 8x = 11x (12 + 11x + 2x2) = 0 Solving 12 + 11x + 2x2 = 0 Solving for variable 'x'. Factor a trinomial. (4 + x)(3 + 2x) = 0Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 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 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Subproblem 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 = {-4, -1.5}
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