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Simplifying 4(2p + q) + -3(2p + -1q) = 0 (2p * 4 + q * 4) + -3(2p + -1q) = 0 (8p + 4q) + -3(2p + -1q) = 0 8p + 4q + (2p * -3 + -1q * -3) = 0 8p + 4q + (-6p + 3q) = 0 Reorder the terms: 8p + -6p + 4q + 3q = 0 Combine like terms: 8p + -6p = 2p 2p + 4q + 3q = 0 Combine like terms: 4q + 3q = 7q 2p + 7q = 0 Solving 2p + 7q = 0 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-7q' to each side of the equation. 2p + 7q + -7q = 0 + -7q Combine like terms: 7q + -7q = 0 2p + 0 = 0 + -7q 2p = 0 + -7q Remove the zero: 2p = -7q Divide each side by '2'. p = -3.5q Simplifying p = -3.5q
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