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Simplifying (n + -6)(4p + 2) = 0 Reorder the terms: (-6 + n)(4p + 2) = 0 Reorder the terms: (-6 + n)(2 + 4p) = 0 Multiply (-6 + n) * (2 + 4p) (-6(2 + 4p) + n(2 + 4p)) = 0 ((2 * -6 + 4p * -6) + n(2 + 4p)) = 0 ((-12 + -24p) + n(2 + 4p)) = 0 (-12 + -24p + (2 * n + 4p * n)) = 0 (-12 + -24p + (2n + 4np)) = 0 Reorder the terms: (-12 + 2n + 4np + -24p) = 0 (-12 + 2n + 4np + -24p) = 0 Solving -12 + 2n + 4np + -24p = 0 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 2n + 4np + 12 + -24p = 0 + 12 Reorder the terms: -12 + 12 + 2n + 4np + -24p = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 2n + 4np + -24p = 0 + 12 2n + 4np + -24p = 0 + 12 Combine like terms: 0 + 12 = 12 2n + 4np + -24p = 12 Add '24p' to each side of the equation. 2n + 4np + -24p + 24p = 12 + 24p Combine like terms: -24p + 24p = 0 2n + 4np + 0 = 12 + 24p 2n + 4np = 12 + 24p Reorder the terms: -12 + 2n + 4np + -24p = 12 + 24p + -12 + -24p Reorder the terms: -12 + 2n + 4np + -24p = 12 + -12 + 24p + -24p Combine like terms: 12 + -12 = 0 -12 + 2n + 4np + -24p = 0 + 24p + -24p -12 + 2n + 4np + -24p = 24p + -24p Combine like terms: 24p + -24p = 0 -12 + 2n + 4np + -24p = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + n + 2np + -12p) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + n + 2np + -12p)' equal to zero and attempt to solve: Simplifying -6 + n + 2np + -12p = 0 Solving -6 + n + 2np + -12p = 0 Move all terms containing n to the left, all other terms to the right. Add '6' to each side of the equation. -6 + n + 2np + 6 + -12p = 0 + 6 Reorder the terms: -6 + 6 + n + 2np + -12p = 0 + 6 Combine like terms: -6 + 6 = 0 0 + n + 2np + -12p = 0 + 6 n + 2np + -12p = 0 + 6 Combine like terms: 0 + 6 = 6 n + 2np + -12p = 6 Add '12p' to each side of the equation. n + 2np + -12p + 12p = 6 + 12p Combine like terms: -12p + 12p = 0 n + 2np + 0 = 6 + 12p n + 2np = 6 + 12p The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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