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Simplifying 3(3x + 2)(x + 4) = 0 Reorder the terms: 3(2 + 3x)(x + 4) = 0 Reorder the terms: 3(2 + 3x)(4 + x) = 0 Multiply (2 + 3x) * (4 + x) 3(2(4 + x) + 3x * (4 + x)) = 0 3((4 * 2 + x * 2) + 3x * (4 + x)) = 0 3((8 + 2x) + 3x * (4 + x)) = 0 3(8 + 2x + (4 * 3x + x * 3x)) = 0 3(8 + 2x + (12x + 3x2)) = 0 Combine like terms: 2x + 12x = 14x 3(8 + 14x + 3x2) = 0 (8 * 3 + 14x * 3 + 3x2 * 3) = 0 (24 + 42x + 9x2) = 0 Solving 24 + 42x + 9x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(8 + 14x + 3x2) = 0 Factor a trinomial. 3((4 + x)(2 + 3x)) = 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 '(2 + 3x)' equal to zero and attempt to solve: Simplifying 2 + 3x = 0 Solving 2 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3x = 0 + -2 3x = 0 + -2 Combine like terms: 0 + -2 = -2 3x = -2 Divide each side by '3'. x = -0.6666666667 Simplifying x = -0.6666666667Solution
x = {-4, -0.6666666667}
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