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Simplifying (3x + 5)(2x + 6) = 0 Reorder the terms: (5 + 3x)(2x + 6) = 0 Reorder the terms: (5 + 3x)(6 + 2x) = 0 Multiply (5 + 3x) * (6 + 2x) (5(6 + 2x) + 3x * (6 + 2x)) = 0 ((6 * 5 + 2x * 5) + 3x * (6 + 2x)) = 0 ((30 + 10x) + 3x * (6 + 2x)) = 0 (30 + 10x + (6 * 3x + 2x * 3x)) = 0 (30 + 10x + (18x + 6x2)) = 0 Combine like terms: 10x + 18x = 28x (30 + 28x + 6x2) = 0 Solving 30 + 28x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(15 + 14x + 3x2) = 0 Factor a trinomial. 2((3 + x)(5 + 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 '(5 + 3x)' equal to zero and attempt to solve: Simplifying 5 + 3x = 0 Solving 5 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3x = 0 + -5 3x = 0 + -5 Combine like terms: 0 + -5 = -5 3x = -5 Divide each side by '3'. x = -1.666666667 Simplifying x = -1.666666667Solution
x = {-3, -1.666666667}
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