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Simplifying (4x + 8)(8x + 6) = 0 Reorder the terms: (8 + 4x)(8x + 6) = 0 Reorder the terms: (8 + 4x)(6 + 8x) = 0 Multiply (8 + 4x) * (6 + 8x) (8(6 + 8x) + 4x * (6 + 8x)) = 0 ((6 * 8 + 8x * 8) + 4x * (6 + 8x)) = 0 ((48 + 64x) + 4x * (6 + 8x)) = 0 (48 + 64x + (6 * 4x + 8x * 4x)) = 0 (48 + 64x + (24x + 32x2)) = 0 Combine like terms: 64x + 24x = 88x (48 + 88x + 32x2) = 0 Solving 48 + 88x + 32x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8'. 8(6 + 11x + 4x2) = 0 Factor a trinomial. 8((2 + x)(3 + 4x)) = 0 Ignore the factor 8.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 + 4x)' equal to zero and attempt to solve: Simplifying 3 + 4x = 0 Solving 3 + 4x = 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 + 4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4x = 0 + -3 4x = 0 + -3 Combine like terms: 0 + -3 = -3 4x = -3 Divide each side by '4'. x = -0.75 Simplifying x = -0.75Solution
x = {-2, -0.75}
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