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Simplifying 2(6p + 3q) + 3(q + -4p) + 5(p + q) = 0 (6p * 2 + 3q * 2) + 3(q + -4p) + 5(p + q) = 0 (12p + 6q) + 3(q + -4p) + 5(p + q) = 0 Reorder the terms: 12p + 6q + 3(-4p + q) + 5(p + q) = 0 12p + 6q + (-4p * 3 + q * 3) + 5(p + q) = 0 12p + 6q + (-12p + 3q) + 5(p + q) = 0 12p + 6q + -12p + 3q + (p * 5 + q * 5) = 0 12p + 6q + -12p + 3q + (5p + 5q) = 0 Reorder the terms: 12p + -12p + 5p + 6q + 3q + 5q = 0 Combine like terms: 12p + -12p = 0 0 + 5p + 6q + 3q + 5q = 0 5p + 6q + 3q + 5q = 0 Combine like terms: 6q + 3q = 9q 5p + 9q + 5q = 0 Combine like terms: 9q + 5q = 14q 5p + 14q = 0 Solving 5p + 14q = 0 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-14q' to each side of the equation. 5p + 14q + -14q = 0 + -14q Combine like terms: 14q + -14q = 0 5p + 0 = 0 + -14q 5p = 0 + -14q Remove the zero: 5p = -14q Divide each side by '5'. p = -2.8q Simplifying p = -2.8q
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