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Simplifying 5p4 + 16p3q + 3p2q2 = 0 Reorder the terms: 3p2q2 + 16p3q + 5p4 = 0 Solving 3p2q2 + 16p3q + 5p4 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), 'p2'. p2(3q2 + 16pq + 5p2) = 0 Factor a trinomial. p2((3q + p)(q + 5p)) = 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 '(3q + p)' equal to zero and attempt to solve: Simplifying 3q + p = 0 Reorder the terms: p + 3q = 0 Solving p + 3q = 0 Move all terms containing p to the left, all other terms to the right. Add '-3q' to each side of the equation. p + 3q + -3q = 0 + -3q Combine like terms: 3q + -3q = 0 p + 0 = 0 + -3q p = 0 + -3q Remove the zero: p = -3q Simplifying p = -3qSubproblem 3
Set the factor '(q + 5p)' equal to zero and attempt to solve: Simplifying q + 5p = 0 Reorder the terms: 5p + q = 0 Solving 5p + q = 0 Move all terms containing p to the left, all other terms to the right. Add '-1q' to each side of the equation. 5p + q + -1q = 0 + -1q Combine like terms: q + -1q = 0 5p + 0 = 0 + -1q 5p = 0 + -1q Remove the zero: 5p = -1q Divide each side by '5'. p = -0.2q Simplifying p = -0.2qSolution
p = {0, -3q, -0.2q}
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