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Simplifying 2pq + 8p + 6q + 24 = 0 Reorder the terms: 24 + 8p + 2pq + 6q = 0 Solving 24 + 8p + 2pq + 6q = 0 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + 8p + 2pq + -24 + 6q = 0 + -24 Reorder the terms: 24 + -24 + 8p + 2pq + 6q = 0 + -24 Combine like terms: 24 + -24 = 0 0 + 8p + 2pq + 6q = 0 + -24 8p + 2pq + 6q = 0 + -24 Combine like terms: 0 + -24 = -24 8p + 2pq + 6q = -24 Add '-6q' to each side of the equation. 8p + 2pq + 6q + -6q = -24 + -6q Combine like terms: 6q + -6q = 0 8p + 2pq + 0 = -24 + -6q 8p + 2pq = -24 + -6q Reorder the terms: 24 + 8p + 2pq + 6q = -24 + -6q + 24 + 6q Reorder the terms: 24 + 8p + 2pq + 6q = -24 + 24 + -6q + 6q Combine like terms: -24 + 24 = 0 24 + 8p + 2pq + 6q = 0 + -6q + 6q 24 + 8p + 2pq + 6q = -6q + 6q Combine like terms: -6q + 6q = 0 24 + 8p + 2pq + 6q = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(12 + 4p + pq + 3q) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(12 + 4p + pq + 3q)' equal to zero and attempt to solve: Simplifying 12 + 4p + pq + 3q = 0 Solving 12 + 4p + pq + 3q = 0 Move all terms containing p to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + 4p + pq + -12 + 3q = 0 + -12 Reorder the terms: 12 + -12 + 4p + pq + 3q = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 4p + pq + 3q = 0 + -12 4p + pq + 3q = 0 + -12 Combine like terms: 0 + -12 = -12 4p + pq + 3q = -12 Add '-3q' to each side of the equation. 4p + pq + 3q + -3q = -12 + -3q Combine like terms: 3q + -3q = 0 4p + pq + 0 = -12 + -3q 4p + pq = -12 + -3q 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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