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Simplifying 4p + 3p2q + -3p + 5p2q + 4pq2 = 0 Reorder the terms: 4p + -3p + 4pq2 + 3p2q + 5p2q = 0 Combine like terms: 4p + -3p = 1p 1p + 4pq2 + 3p2q + 5p2q = 0 Combine like terms: 3p2q + 5p2q = 8p2q 1p + 4pq2 + 8p2q = 0 Solving 1p + 4pq2 + 8p2q = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), 'p'. p(1 + 4q2 + 8pq) = 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 '(1 + 4q2 + 8pq)' equal to zero and attempt to solve: Simplifying 1 + 4q2 + 8pq = 0 Reorder the terms: 1 + 8pq + 4q2 = 0 Solving 1 + 8pq + 4q2 = 0 Move all terms containing p to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + 8pq + -1 + 4q2 = 0 + -1 Reorder the terms: 1 + -1 + 8pq + 4q2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 8pq + 4q2 = 0 + -1 8pq + 4q2 = 0 + -1 Combine like terms: 0 + -1 = -1 8pq + 4q2 = -1 Add '-4q2' to each side of the equation. 8pq + 4q2 + -4q2 = -1 + -4q2 Combine like terms: 4q2 + -4q2 = 0 8pq + 0 = -1 + -4q2 8pq = -1 + -4q2 Divide each side by '8q'. p = -0.125q-1 + -0.5q Simplifying p = -0.125q-1 + -0.5qSolution
p = {0, -0.125q-1 + -0.5q}
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