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Simplifying (2x + 6)(3x + 2) = 0 Reorder the terms: (6 + 2x)(3x + 2) = 0 Reorder the terms: (6 + 2x)(2 + 3x) = 0 Multiply (6 + 2x) * (2 + 3x) (6(2 + 3x) + 2x * (2 + 3x)) = 0 ((2 * 6 + 3x * 6) + 2x * (2 + 3x)) = 0 ((12 + 18x) + 2x * (2 + 3x)) = 0 (12 + 18x + (2 * 2x + 3x * 2x)) = 0 (12 + 18x + (4x + 6x2)) = 0 Combine like terms: 18x + 4x = 22x (12 + 22x + 6x2) = 0 Solving 12 + 22x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(6 + 11x + 3x2) = 0 Factor a trinomial. 2((3 + x)(2 + 3x)) = 0 Ignore the factor 2.Subproblem 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 '(2 + 3x)' equal to zero and attempt to solve: Simplifying 2 + 3x = 0 Solving 2 + 3x = 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 + 3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3x = 0 + -2 3x = 0 + -2 Combine like terms: 0 + -2 = -2 3x = -2 Divide each side by '3'. x = -0.6666666667 Simplifying x = -0.6666666667Solution
x = {-3, -0.6666666667}
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