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Simplifying (3x + 12)(x + 4) = 0 Reorder the terms: (12 + 3x)(x + 4) = 0 Reorder the terms: (12 + 3x)(4 + x) = 0 Multiply (12 + 3x) * (4 + x) (12(4 + x) + 3x * (4 + x)) = 0 ((4 * 12 + x * 12) + 3x * (4 + x)) = 0 ((48 + 12x) + 3x * (4 + x)) = 0 (48 + 12x + (4 * 3x + x * 3x)) = 0 (48 + 12x + (12x + 3x2)) = 0 Combine like terms: 12x + 12x = 24x (48 + 24x + 3x2) = 0 Solving 48 + 24x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(16 + 8x + x2) = 0 Factor a trinomial. 3((4 + x)(4 + x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 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 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 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 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Solution
x = {-4, -4}
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