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Simplifying (3x + 1)(2x + 6) = 0 Reorder the terms: (1 + 3x)(2x + 6) = 0 Reorder the terms: (1 + 3x)(6 + 2x) = 0 Multiply (1 + 3x) * (6 + 2x) (1(6 + 2x) + 3x * (6 + 2x)) = 0 ((6 * 1 + 2x * 1) + 3x * (6 + 2x)) = 0 ((6 + 2x) + 3x * (6 + 2x)) = 0 (6 + 2x + (6 * 3x + 2x * 3x)) = 0 (6 + 2x + (18x + 6x2)) = 0 Combine like terms: 2x + 18x = 20x (6 + 20x + 6x2) = 0 Solving 6 + 20x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 10x + 3x2) = 0 Factor a trinomial. 2((3 + x)(1 + 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 '(1 + 3x)' equal to zero and attempt to solve: Simplifying 1 + 3x = 0 Solving 1 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x = 0 + -1 3x = 0 + -1 Combine like terms: 0 + -1 = -1 3x = -1 Divide each side by '3'. x = -0.3333333333 Simplifying x = -0.3333333333Solution
x = {-3, -0.3333333333}
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