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Simplifying (x + 5)(4x + 12) = 0 Reorder the terms: (5 + x)(4x + 12) = 0 Reorder the terms: (5 + x)(12 + 4x) = 0 Multiply (5 + x) * (12 + 4x) (5(12 + 4x) + x(12 + 4x)) = 0 ((12 * 5 + 4x * 5) + x(12 + 4x)) = 0 ((60 + 20x) + x(12 + 4x)) = 0 (60 + 20x + (12 * x + 4x * x)) = 0 (60 + 20x + (12x + 4x2)) = 0 Combine like terms: 20x + 12x = 32x (60 + 32x + 4x2) = 0 Solving 60 + 32x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(15 + 8x + x2) = 0 Factor a trinomial. 4((5 + x)(3 + x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Solution
x = {-5, -3}
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