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Simplifying (8x + 4)(6x * 2 + 4x + 4) = 0 Reorder the terms: (4 + 8x)(6x * 2 + 4x + 4) = 0 Reorder the terms for easier multiplication: (4 + 8x)(6 * 2x + 4x + 4) = 0 Multiply 6 * 2 (4 + 8x)(12x + 4x + 4) = 0 Reorder the terms: (4 + 8x)(4 + 12x + 4x) = 0 Combine like terms: 12x + 4x = 16x (4 + 8x)(4 + 16x) = 0 Multiply (4 + 8x) * (4 + 16x) (4(4 + 16x) + 8x * (4 + 16x)) = 0 ((4 * 4 + 16x * 4) + 8x * (4 + 16x)) = 0 ((16 + 64x) + 8x * (4 + 16x)) = 0 (16 + 64x + (4 * 8x + 16x * 8x)) = 0 (16 + 64x + (32x + 128x2)) = 0 Combine like terms: 64x + 32x = 96x (16 + 96x + 128x2) = 0 Solving 16 + 96x + 128x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '16'. 16(1 + 6x + 8x2) = 0 Factor a trinomial. 16((1 + 2x)(1 + 4x)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5Subproblem 2
Set the factor '(1 + 4x)' equal to zero and attempt to solve: Simplifying 1 + 4x = 0 Solving 1 + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4x = 0 + -1 4x = 0 + -1 Combine like terms: 0 + -1 = -1 4x = -1 Divide each side by '4'. x = -0.25 Simplifying x = -0.25Solution
x = {-0.5, -0.25}
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