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Simplifying 13p4 + 27p3q + 2p2q2 = 0 Reorder the terms: 2p2q2 + 27p3q + 13p4 = 0 Solving 2p2q2 + 27p3q + 13p4 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), 'p2'. p2(2q2 + 27pq + 13p2) = 0 Factor a trinomial. p2((2q + p)(q + 13p)) = 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 '(2q + p)' equal to zero and attempt to solve: Simplifying 2q + p = 0 Reorder the terms: p + 2q = 0 Solving p + 2q = 0 Move all terms containing p to the left, all other terms to the right. Add '-2q' to each side of the equation. p + 2q + -2q = 0 + -2q Combine like terms: 2q + -2q = 0 p + 0 = 0 + -2q p = 0 + -2q Remove the zero: p = -2q Simplifying p = -2qSubproblem 3
Set the factor '(q + 13p)' equal to zero and attempt to solve: Simplifying q + 13p = 0 Reorder the terms: 13p + q = 0 Solving 13p + q = 0 Move all terms containing p to the left, all other terms to the right. Add '-1q' to each side of the equation. 13p + q + -1q = 0 + -1q Combine like terms: q + -1q = 0 13p + 0 = 0 + -1q 13p = 0 + -1q Remove the zero: 13p = -1q Divide each side by '13'. p = -0.07692307692q Simplifying p = -0.07692307692qSolution
p = {0, -2q, -0.07692307692q}
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