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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 = -2x (-48 + -2x + 6x2) = 0 Solving -48 + -2x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-24 + -1x + 3x2) = 0 Factor a trinomial. 2((-8 + -3x)(3 + -1x)) = 0 Ignore the factor 2.Subproblem 1
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 = -2.666666667Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-2.666666667, 3}
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