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Simplifying (12p + 7q)(-2p + 9q) = 0 Multiply (12p + 7q) * (-2p + 9q) (12p * (-2p + 9q) + 7q * (-2p + 9q)) = 0 ((-2p * 12p + 9q * 12p) + 7q * (-2p + 9q)) = 0 Reorder the terms: ((108pq + -24p2) + 7q * (-2p + 9q)) = 0 ((108pq + -24p2) + 7q * (-2p + 9q)) = 0 (108pq + -24p2 + (-2p * 7q + 9q * 7q)) = 0 (108pq + -24p2 + (-14pq + 63q2)) = 0 Reorder the terms: (108pq + -14pq + -24p2 + 63q2) = 0 Combine like terms: 108pq + -14pq = 94pq (94pq + -24p2 + 63q2) = 0 Solving 94pq + -24p2 + 63q2 = 0 Solving for variable 'p'. Factor a trinomial. (-12p + -7q)(2p + -9q) = 0Subproblem 1
Set the factor '(-12p + -7q)' equal to zero and attempt to solve: Simplifying -12p + -7q = 0 Solving -12p + -7q = 0 Move all terms containing p to the left, all other terms to the right. Add '7q' to each side of the equation. -12p + -7q + 7q = 0 + 7q Combine like terms: -7q + 7q = 0 -12p + 0 = 0 + 7q -12p = 0 + 7q Remove the zero: -12p = 7q Divide each side by '-12'. p = -0.5833333333q Simplifying p = -0.5833333333qSubproblem 2
Set the factor '(2p + -9q)' equal to zero and attempt to solve: Simplifying 2p + -9q = 0 Solving 2p + -9q = 0 Move all terms containing p to the left, all other terms to the right. Add '9q' to each side of the equation. 2p + -9q + 9q = 0 + 9q Combine like terms: -9q + 9q = 0 2p + 0 = 0 + 9q 2p = 0 + 9q Remove the zero: 2p = 9q Divide each side by '2'. p = 4.5q Simplifying p = 4.5qSolution
p = {-0.5833333333q, 4.5q}
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