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Simplifying (2x + 12)(3x + 4) = 0 Reorder the terms: (12 + 2x)(3x + 4) = 0 Reorder the terms: (12 + 2x)(4 + 3x) = 0 Multiply (12 + 2x) * (4 + 3x) (12(4 + 3x) + 2x * (4 + 3x)) = 0 ((4 * 12 + 3x * 12) + 2x * (4 + 3x)) = 0 ((48 + 36x) + 2x * (4 + 3x)) = 0 (48 + 36x + (4 * 2x + 3x * 2x)) = 0 (48 + 36x + (8x + 6x2)) = 0 Combine like terms: 36x + 8x = 44x (48 + 44x + 6x2) = 0 Solving 48 + 44x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(24 + 22x + 3x2) = 0 Factor a trinomial. 2((6 + x)(4 + 3x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Subproblem 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 = {-6, -1.333333333}
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