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Simplifying (3x + 6)(2x + 3) = 0 Reorder the terms: (6 + 3x)(2x + 3) = 0 Reorder the terms: (6 + 3x)(3 + 2x) = 0 Multiply (6 + 3x) * (3 + 2x) (6(3 + 2x) + 3x * (3 + 2x)) = 0 ((3 * 6 + 2x * 6) + 3x * (3 + 2x)) = 0 ((18 + 12x) + 3x * (3 + 2x)) = 0 (18 + 12x + (3 * 3x + 2x * 3x)) = 0 (18 + 12x + (9x + 6x2)) = 0 Combine like terms: 12x + 9x = 21x (18 + 21x + 6x2) = 0 Solving 18 + 21x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(6 + 7x + 2x2) = 0 Factor a trinomial. 3((2 + x)(3 + 2x)) = 0 Ignore the factor 3.Subproblem 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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