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Simplifying (3x + 4)(2x + 6) = 0 Reorder the terms: (4 + 3x)(2x + 6) = 0 Reorder the terms: (4 + 3x)(6 + 2x) = 0 Multiply (4 + 3x) * (6 + 2x) (4(6 + 2x) + 3x * (6 + 2x)) = 0 ((6 * 4 + 2x * 4) + 3x * (6 + 2x)) = 0 ((24 + 8x) + 3x * (6 + 2x)) = 0 (24 + 8x + (6 * 3x + 2x * 3x)) = 0 (24 + 8x + (18x + 6x2)) = 0 Combine like terms: 8x + 18x = 26x (24 + 26x + 6x2) = 0 Solving 24 + 26x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(12 + 13x + 3x2) = 0 Factor a trinomial. 2((3 + x)(4 + 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 '(4 + 3x)' equal to zero and attempt to solve: Simplifying 4 + 3x = 0 Solving 4 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3x = 0 + -4 3x = 0 + -4 Combine like terms: 0 + -4 = -4 3x = -4 Divide each side by '3'. x = -1.333333333 Simplifying x = -1.333333333Solution
x = {-3, -1.333333333}
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