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Simplifying 3p4 + 7p3q + 4p2q2 = 0 Reorder the terms: 4p2q2 + 7p3q + 3p4 = 0 Solving 4p2q2 + 7p3q + 3p4 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), 'p2'. p2(4q2 + 7pq + 3p2) = 0 Factor a trinomial. p2((4q + 3p)(q + p)) = 0Subproblem 1
Set the factor 'p2' equal to zero and attempt to solve: Simplifying p2 = 0 Solving p2 = 0 Move all terms containing p to the left, all other terms to the right. Simplifying p2 = 0 Take the square root of each side: p = {0}Subproblem 2
Set the factor '(4q + 3p)' equal to zero and attempt to solve: Simplifying 4q + 3p = 0 Reorder the terms: 3p + 4q = 0 Solving 3p + 4q = 0 Move all terms containing p to the left, all other terms to the right. Add '-4q' to each side of the equation. 3p + 4q + -4q = 0 + -4q Combine like terms: 4q + -4q = 0 3p + 0 = 0 + -4q 3p = 0 + -4q Remove the zero: 3p = -4q Divide each side by '3'. p = -1.333333333q Simplifying p = -1.333333333qSubproblem 3
Set the factor '(q + p)' equal to zero and attempt to solve: Simplifying q + p = 0 Reorder the terms: p + q = 0 Solving p + q = 0 Move all terms containing p to the left, all other terms to the right. Add '-1q' to each side of the equation. p + q + -1q = 0 + -1q Combine like terms: q + -1q = 0 p + 0 = 0 + -1q p = 0 + -1q Remove the zero: p = -1q Simplifying p = -1qSolution
p = {0, -1.333333333q, -1q}
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