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Simplifying 4(2p + q) + 3(2p + q) = 0 (2p * 4 + q * 4) + 3(2p + q) = 0 (8p + 4q) + 3(2p + q) = 0 8p + 4q + (2p * 3 + q * 3) = 0 8p + 4q + (6p + 3q) = 0 Reorder the terms: 8p + 6p + 4q + 3q = 0 Combine like terms: 8p + 6p = 14p 14p + 4q + 3q = 0 Combine like terms: 4q + 3q = 7q 14p + 7q = 0 Solving 14p + 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. 14p + 7q + -7q = 0 + -7q Combine like terms: 7q + -7q = 0 14p + 0 = 0 + -7q 14p = 0 + -7q Remove the zero: 14p = -7q Divide each side by '14'. p = -0.5q Simplifying p = -0.5q
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