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Simplifying p3 + -6p2q + -40pq2 = 0 Reorder the terms: -40pq2 + -6p2q + p3 = 0 Solving -40pq2 + -6p2q + p3 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), 'p'. p(-40q2 + -6pq + p2) = 0 Factor a trinomial. p((-4q + -1p)(10q + -1p)) = 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 '(-4q + -1p)' equal to zero and attempt to solve: Simplifying -4q + -1p = 0 Reorder the terms: -1p + -4q = 0 Solving -1p + -4q = 0 Move all terms containing p to the left, all other terms to the right. Add '4q' to each side of the equation. -1p + -4q + 4q = 0 + 4q Combine like terms: -4q + 4q = 0 -1p + 0 = 0 + 4q -1p = 0 + 4q Remove the zero: -1p = 4q Divide each side by '-1'. p = -4q Simplifying p = -4qSubproblem 3
Set the factor '(10q + -1p)' equal to zero and attempt to solve: Simplifying 10q + -1p = 0 Reorder the terms: -1p + 10q = 0 Solving -1p + 10q = 0 Move all terms containing p to the left, all other terms to the right. Add '-10q' to each side of the equation. -1p + 10q + -10q = 0 + -10q Combine like terms: 10q + -10q = 0 -1p + 0 = 0 + -10q -1p = 0 + -10q Remove the zero: -1p = -10q Divide each side by '-1'. p = 10q Simplifying p = 10qSolution
p = {0, -4q, 10q}
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