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Simplifying -12p2 + -8pq + 15q2 = 0 Reorder the terms: -8pq + -12p2 + 15q2 = 0 Solving -8pq + -12p2 + 15q2 = 0 Solving for variable 'p'. Factor a trinomial. (-2p + -3q)(6p + -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 '(6p + -5q)' equal to zero and attempt to solve: Simplifying 6p + -5q = 0 Solving 6p + -5q = 0 Move all terms containing p to the left, all other terms to the right. Add '5q' to each side of the equation. 6p + -5q + 5q = 0 + 5q Combine like terms: -5q + 5q = 0 6p + 0 = 0 + 5q 6p = 0 + 5q Remove the zero: 6p = 5q Divide each side by '6'. p = 0.8333333333q Simplifying p = 0.8333333333qSolution
p = {-1.5q, 0.8333333333q}
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