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Simplifying 12p4 + 61p3q + 5p2q2 = 0 Reorder the terms: 5p2q2 + 61p3q + 12p4 = 0 Solving 5p2q2 + 61p3q + 12p4 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), 'p2'. p2(5q2 + 61pq + 12p2) = 0 Factor a trinomial. p2((5q + p)(q + 12p)) = 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 '(5q + p)' equal to zero and attempt to solve: Simplifying 5q + p = 0 Reorder the terms: p + 5q = 0 Solving p + 5q = 0 Move all terms containing p to the left, all other terms to the right. Add '-5q' to each side of the equation. p + 5q + -5q = 0 + -5q Combine like terms: 5q + -5q = 0 p + 0 = 0 + -5q p = 0 + -5q Remove the zero: p = -5q Simplifying p = -5qSubproblem 3
Set the factor '(q + 12p)' equal to zero and attempt to solve: Simplifying q + 12p = 0 Reorder the terms: 12p + q = 0 Solving 12p + q = 0 Move all terms containing p to the left, all other terms to the right. Add '-1q' to each side of the equation. 12p + q + -1q = 0 + -1q Combine like terms: q + -1q = 0 12p + 0 = 0 + -1q 12p = 0 + -1q Remove the zero: 12p = -1q Divide each side by '12'. p = -0.08333333333q Simplifying p = -0.08333333333qSolution
p = {0, -5q, -0.08333333333q}
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