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Simplifying (4x + 6)(2x + 4) = 0 Reorder the terms: (6 + 4x)(2x + 4) = 0 Reorder the terms: (6 + 4x)(4 + 2x) = 0 Multiply (6 + 4x) * (4 + 2x) (6(4 + 2x) + 4x * (4 + 2x)) = 0 ((4 * 6 + 2x * 6) + 4x * (4 + 2x)) = 0 ((24 + 12x) + 4x * (4 + 2x)) = 0 (24 + 12x + (4 * 4x + 2x * 4x)) = 0 (24 + 12x + (16x + 8x2)) = 0 Combine like terms: 12x + 16x = 28x (24 + 28x + 8x2) = 0 Solving 24 + 28x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(6 + 7x + 2x2) = 0 Factor a trinomial. 4((2 + x)(3 + 2x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 2
Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 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 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Solution
x = {-2, -1.5}
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