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Simplifying 2p2 + 13pq + 15q2 = 0 Reorder the terms: 13pq + 2p2 + 15q2 = 0 Solving 13pq + 2p2 + 15q2 = 0 Solving for variable 'p'. Factor a trinomial. (2p + 3q)(p + 5q) = 0Subproblem 1
Set the factor '(2p + 3q)' equal to zero and attempt to solve: Simplifying 2p + 3q = 0 Solving 2p + 3q = 0 Move all terms containing p to the left, all other terms to the right. Add '-3q' to each side of the equation. 2p + 3q + -3q = 0 + -3q Combine like terms: 3q + -3q = 0 2p + 0 = 0 + -3q 2p = 0 + -3q Remove the zero: 2p = -3q Divide each side by '2'. p = -1.5q Simplifying p = -1.5qSubproblem 2
Set the factor '(p + 5q)' equal to zero and attempt to solve: Simplifying 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 = -5qSolution
p = {-1.5q, -5q}
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