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Simplifying 4pq + 8p + -8q + -16 = 0 Reorder the terms: -16 + 8p + 4pq + -8q = 0 Solving -16 + 8p + 4pq + -8q = 0 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 8p + 4pq + 16 + -8q = 0 + 16 Reorder the terms: -16 + 16 + 8p + 4pq + -8q = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 8p + 4pq + -8q = 0 + 16 8p + 4pq + -8q = 0 + 16 Combine like terms: 0 + 16 = 16 8p + 4pq + -8q = 16 Add '8q' to each side of the equation. 8p + 4pq + -8q + 8q = 16 + 8q Combine like terms: -8q + 8q = 0 8p + 4pq + 0 = 16 + 8q 8p + 4pq = 16 + 8q Reorder the terms: -16 + 8p + 4pq + -8q = 16 + 8q + -16 + -8q Reorder the terms: -16 + 8p + 4pq + -8q = 16 + -16 + 8q + -8q Combine like terms: 16 + -16 = 0 -16 + 8p + 4pq + -8q = 0 + 8q + -8q -16 + 8p + 4pq + -8q = 8q + -8q Combine like terms: 8q + -8q = 0 -16 + 8p + 4pq + -8q = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-4 + 2p + pq + -2q) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-4 + 2p + pq + -2q)' equal to zero and attempt to solve: Simplifying -4 + 2p + pq + -2q = 0 Solving -4 + 2p + pq + -2q = 0 Move all terms containing p to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 2p + pq + 4 + -2q = 0 + 4 Reorder the terms: -4 + 4 + 2p + pq + -2q = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 2p + pq + -2q = 0 + 4 2p + pq + -2q = 0 + 4 Combine like terms: 0 + 4 = 4 2p + pq + -2q = 4 Add '2q' to each side of the equation. 2p + pq + -2q + 2q = 4 + 2q Combine like terms: -2q + 2q = 0 2p + pq + 0 = 4 + 2q 2p + pq = 4 + 2q 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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