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Simplifying 4pq(3 + -1q) + 2p(q + -3) + -7q(p + -2pq) + -2p(5q2 + 3) = 0 (3 * 4pq + -1q * 4pq) + 2p(q + -3) + -7q(p + -2pq) + -2p(5q2 + 3) = 0 (12pq + -4pq2) + 2p(q + -3) + -7q(p + -2pq) + -2p(5q2 + 3) = 0 Reorder the terms: 12pq + -4pq2 + 2p(-3 + q) + -7q(p + -2pq) + -2p(5q2 + 3) = 0 12pq + -4pq2 + (-3 * 2p + q * 2p) + -7q(p + -2pq) + -2p(5q2 + 3) = 0 12pq + -4pq2 + (-6p + 2pq) + -7q(p + -2pq) + -2p(5q2 + 3) = 0 12pq + -4pq2 + -6p + 2pq + (p * -7q + -2pq * -7q) + -2p(5q2 + 3) = 0 12pq + -4pq2 + -6p + 2pq + (-7pq + 14pq2) + -2p(5q2 + 3) = 0 Reorder the terms: 12pq + -4pq2 + -6p + 2pq + -7pq + 14pq2 + -2p(3 + 5q2) = 0 12pq + -4pq2 + -6p + 2pq + -7pq + 14pq2 + (3 * -2p + 5q2 * -2p) = 0 12pq + -4pq2 + -6p + 2pq + -7pq + 14pq2 + (-6p + -10pq2) = 0 Reorder the terms: -6p + -6p + 12pq + 2pq + -7pq + -4pq2 + 14pq2 + -10pq2 = 0 Combine like terms: -6p + -6p = -12p -12p + 12pq + 2pq + -7pq + -4pq2 + 14pq2 + -10pq2 = 0 Combine like terms: 12pq + 2pq = 14pq -12p + 14pq + -7pq + -4pq2 + 14pq2 + -10pq2 = 0 Combine like terms: 14pq + -7pq = 7pq -12p + 7pq + -4pq2 + 14pq2 + -10pq2 = 0 Combine like terms: -4pq2 + 14pq2 = 10pq2 -12p + 7pq + 10pq2 + -10pq2 = 0 Combine like terms: 10pq2 + -10pq2 = 0 -12p + 7pq + 0 = 0 -12p + 7pq = 0 Solving -12p + 7pq = 0 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'p'. p(-12 + 7q) = 0Subproblem 1
Set the factor 'p' equal to zero and attempt to solve: Simplifying p = 0 Solving p = 0 Move all terms containing p to the left, all other terms to the right. Simplifying p = 0Subproblem 2
Set the factor '(-12 + 7q)' equal to zero and attempt to solve: Simplifying -12 + 7q = 0 Solving -12 + 7q = 0 Move all terms containing p to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + 7q = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 7q = 0 + 12 7q = 0 + 12 Combine like terms: 0 + 12 = 12 7q = 12 Add '-7q' to each side of the equation. 7q + -7q = 12 + -7q Combine like terms: 7q + -7q = 0 0 = 12 + -7q Simplifying 0 = 12 + -7q The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
p = {0}
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