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Simplifying (3x + 2)(6x + 3) = 0 Reorder the terms: (2 + 3x)(6x + 3) = 0 Reorder the terms: (2 + 3x)(3 + 6x) = 0 Multiply (2 + 3x) * (3 + 6x) (2(3 + 6x) + 3x * (3 + 6x)) = 0 ((3 * 2 + 6x * 2) + 3x * (3 + 6x)) = 0 ((6 + 12x) + 3x * (3 + 6x)) = 0 (6 + 12x + (3 * 3x + 6x * 3x)) = 0 (6 + 12x + (9x + 18x2)) = 0 Combine like terms: 12x + 9x = 21x (6 + 21x + 18x2) = 0 Solving 6 + 21x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(2 + 7x + 6x2) = 0 Factor a trinomial. 3((2 + 3x)(1 + 2x)) = 0 Ignore the factor 3.Subproblem 1
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 = -0.6666666667Subproblem 2
Set the factor '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 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 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5Solution
x = {-0.6666666667, -0.5}
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