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Simplifying 5(3p + -2q) + 2(q + 2p) = 0 (3p * 5 + -2q * 5) + 2(q + 2p) = 0 (15p + -10q) + 2(q + 2p) = 0 Reorder the terms: 15p + -10q + 2(2p + q) = 0 15p + -10q + (2p * 2 + q * 2) = 0 15p + -10q + (4p + 2q) = 0 Reorder the terms: 15p + 4p + -10q + 2q = 0 Combine like terms: 15p + 4p = 19p 19p + -10q + 2q = 0 Combine like terms: -10q + 2q = -8q 19p + -8q = 0 Solving 19p + -8q = 0 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '8q' to each side of the equation. 19p + -8q + 8q = 0 + 8q Combine like terms: -8q + 8q = 0 19p + 0 = 0 + 8q 19p = 0 + 8q Remove the zero: 19p = 8q Divide each side by '19'. p = 0.4210526316q Simplifying p = 0.4210526316q
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