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Simplifying (3x + 6)(3x + 1) = 0 Reorder the terms: (6 + 3x)(3x + 1) = 0 Reorder the terms: (6 + 3x)(1 + 3x) = 0 Multiply (6 + 3x) * (1 + 3x) (6(1 + 3x) + 3x * (1 + 3x)) = 0 ((1 * 6 + 3x * 6) + 3x * (1 + 3x)) = 0 ((6 + 18x) + 3x * (1 + 3x)) = 0 (6 + 18x + (1 * 3x + 3x * 3x)) = 0 (6 + 18x + (3x + 9x2)) = 0 Combine like terms: 18x + 3x = 21x (6 + 21x + 9x2) = 0 Solving 6 + 21x + 9x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(2 + 7x + 3x2) = 0 Factor a trinomial. 3((2 + x)(1 + 3x)) = 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 '(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 = {-2, -0.3333333333}
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