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Simplifying 4(3p + 5q) + -3(2p + -1q) = 0 (3p * 4 + 5q * 4) + -3(2p + -1q) = 0 (12p + 20q) + -3(2p + -1q) = 0 12p + 20q + (2p * -3 + -1q * -3) = 0 12p + 20q + (-6p + 3q) = 0 Reorder the terms: 12p + -6p + 20q + 3q = 0 Combine like terms: 12p + -6p = 6p 6p + 20q + 3q = 0 Combine like terms: 20q + 3q = 23q 6p + 23q = 0 Solving 6p + 23q = 0 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-23q' to each side of the equation. 6p + 23q + -23q = 0 + -23q Combine like terms: 23q + -23q = 0 6p + 0 = 0 + -23q 6p = 0 + -23q Remove the zero: 6p = -23q Divide each side by '6'. p = -3.833333333q Simplifying p = -3.833333333q
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