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Simplifying (3x + 3)(6x + -8) = 0 Reorder the terms: (3 + 3x)(6x + -8) = 0 Reorder the terms: (3 + 3x)(-8 + 6x) = 0 Multiply (3 + 3x) * (-8 + 6x) (3(-8 + 6x) + 3x * (-8 + 6x)) = 0 ((-8 * 3 + 6x * 3) + 3x * (-8 + 6x)) = 0 ((-24 + 18x) + 3x * (-8 + 6x)) = 0 (-24 + 18x + (-8 * 3x + 6x * 3x)) = 0 (-24 + 18x + (-24x + 18x2)) = 0 Combine like terms: 18x + -24x = -6x (-24 + -6x + 18x2) = 0 Solving -24 + -6x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-4 + -1x + 3x2) = 0 Factor a trinomial. 6((-1 + -1x)(4 + -3x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 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 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1Subproblem 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 = {-1, 1.333333333}
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