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Simplifying (x + 2)(x + 4) = x2 + px + 8 Reorder the terms: (2 + x)(x + 4) = x2 + px + 8 Reorder the terms: (2 + x)(4 + x) = x2 + px + 8 Multiply (2 + x) * (4 + x) (2(4 + x) + x(4 + x)) = x2 + px + 8 ((4 * 2 + x * 2) + x(4 + x)) = x2 + px + 8 ((8 + 2x) + x(4 + x)) = x2 + px + 8 (8 + 2x + (4 * x + x * x)) = x2 + px + 8 (8 + 2x + (4x + x2)) = x2 + px + 8 Combine like terms: 2x + 4x = 6x (8 + 6x + x2) = x2 + px + 8 Reorder the terms: 8 + 6x + x2 = 8 + px + x2 Add '-8' to each side of the equation. 8 + 6x + -8 + x2 = 8 + px + -8 + x2 Reorder the terms: 8 + -8 + 6x + x2 = 8 + px + -8 + x2 Combine like terms: 8 + -8 = 0 0 + 6x + x2 = 8 + px + -8 + x2 6x + x2 = 8 + px + -8 + x2 Reorder the terms: 6x + x2 = 8 + -8 + px + x2 Combine like terms: 8 + -8 = 0 6x + x2 = 0 + px + x2 6x + x2 = px + x2 Add '-1x2' to each side of the equation. 6x + x2 + -1x2 = px + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 6x + 0 = px + x2 + -1x2 6x = px + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 6x = px + 0 6x = px Solving 6x = px Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1px' to each side of the equation. -1px + 6x = px + -1px Combine like terms: px + -1px = 0 -1px + 6x = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-1p + 6) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-1p + 6)' equal to zero and attempt to solve: Simplifying -1p + 6 = 0 Reorder the terms: 6 + -1p = 0 Solving 6 + -1p = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1p = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1p = 0 + -6 -1p = 0 + -6 Combine like terms: 0 + -6 = -6 -1p = -6 Add 'p' to each side of the equation. -1p + p = -6 + p Combine like terms: -1p + p = 0 0 = -6 + p Simplifying 0 = -6 + p The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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