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Simplifying (2x + 6)(3x + -4) = 0 Reorder the terms: (6 + 2x)(3x + -4) = 0 Reorder the terms: (6 + 2x)(-4 + 3x) = 0 Multiply (6 + 2x) * (-4 + 3x) (6(-4 + 3x) + 2x * (-4 + 3x)) = 0 ((-4 * 6 + 3x * 6) + 2x * (-4 + 3x)) = 0 ((-24 + 18x) + 2x * (-4 + 3x)) = 0 (-24 + 18x + (-4 * 2x + 3x * 2x)) = 0 (-24 + 18x + (-8x + 6x2)) = 0 Combine like terms: 18x + -8x = 10x (-24 + 10x + 6x2) = 0 Solving -24 + 10x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + 5x + 3x2) = 0 Factor a trinomial. 2((-3 + -1x)(4 + -3x)) = 0 Ignore the factor 2.Subproblem 1
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 = -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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