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Simplifying (3x + 8)(2x + 6) = 0 Reorder the terms: (8 + 3x)(2x + 6) = 0 Reorder the terms: (8 + 3x)(6 + 2x) = 0 Multiply (8 + 3x) * (6 + 2x) (8(6 + 2x) + 3x * (6 + 2x)) = 0 ((6 * 8 + 2x * 8) + 3x * (6 + 2x)) = 0 ((48 + 16x) + 3x * (6 + 2x)) = 0 (48 + 16x + (6 * 3x + 2x * 3x)) = 0 (48 + 16x + (18x + 6x2)) = 0 Combine like terms: 16x + 18x = 34x (48 + 34x + 6x2) = 0 Solving 48 + 34x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(24 + 17x + 3x2) = 0 Factor a trinomial. 2((3 + x)(8 + 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 '(8 + 3x)' equal to zero and attempt to solve: Simplifying 8 + 3x = 0 Solving 8 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 3x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 3x = 0 + -8 3x = 0 + -8 Combine like terms: 0 + -8 = -8 3x = -8 Divide each side by '3'. x = -2.666666667 Simplifying x = -2.666666667Solution
x = {-3, -2.666666667}
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