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Simplifying (x + 5)(2x + 3) = 0 Reorder the terms: (5 + x)(2x + 3) = 0 Reorder the terms: (5 + x)(3 + 2x) = 0 Multiply (5 + x) * (3 + 2x) (5(3 + 2x) + x(3 + 2x)) = 0 ((3 * 5 + 2x * 5) + x(3 + 2x)) = 0 ((15 + 10x) + x(3 + 2x)) = 0 (15 + 10x + (3 * x + 2x * x)) = 0 (15 + 10x + (3x + 2x2)) = 0 Combine like terms: 10x + 3x = 13x (15 + 13x + 2x2) = 0 Solving 15 + 13x + 2x2 = 0 Solving for variable 'x'. Factor a trinomial. (5 + x)(3 + 2x) = 0Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 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 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 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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