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Simplifying 5(3p + -2q) + -2(3p + 2q) = 0 (3p * 5 + -2q * 5) + -2(3p + 2q) = 0 (15p + -10q) + -2(3p + 2q) = 0 15p + -10q + (3p * -2 + 2q * -2) = 0 15p + -10q + (-6p + -4q) = 0 Reorder the terms: 15p + -6p + -10q + -4q = 0 Combine like terms: 15p + -6p = 9p 9p + -10q + -4q = 0 Combine like terms: -10q + -4q = -14q 9p + -14q = 0 Solving 9p + -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. 9p + -14q + 14q = 0 + 14q Combine like terms: -14q + 14q = 0 9p + 0 = 0 + 14q 9p = 0 + 14q Remove the zero: 9p = 14q Divide each side by '9'. p = 1.555555556q Simplifying p = 1.555555556q
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