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Simplifying 5(p + q) + -1(4p + -8q) = 0 (p * 5 + q * 5) + -1(4p + -8q) = 0 (5p + 5q) + -1(4p + -8q) = 0 5p + 5q + (4p * -1 + -8q * -1) = 0 5p + 5q + (-4p + 8q) = 0 Reorder the terms: 5p + -4p + 5q + 8q = 0 Combine like terms: 5p + -4p = 1p 1p + 5q + 8q = 0 Combine like terms: 5q + 8q = 13q 1p + 13q = 0 Solving 1p + 13q = 0 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-13q' to each side of the equation. 1p + 13q + -13q = 0 + -13q Combine like terms: 13q + -13q = 0 1p + 0 = 0 + -13q 1p = 0 + -13q Remove the zero: 1p = -13q Divide each side by '1'. p = -13q Simplifying p = -13q
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