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Simplifying (3p + q + 3r) + -1(5r + -2q + p) = 0 Remove parenthesis around (3p + q + 3r) 3p + q + 3r + -1(5r + -2q + p) = 0 Reorder the terms: 3p + q + 3r + -1(p + -2q + 5r) = 0 3p + q + 3r + (p * -1 + -2q * -1 + 5r * -1) = 0 3p + q + 3r + (-1p + 2q + -5r) = 0 Reorder the terms: 3p + -1p + q + 2q + 3r + -5r = 0 Combine like terms: 3p + -1p = 2p 2p + q + 2q + 3r + -5r = 0 Combine like terms: q + 2q = 3q 2p + 3q + 3r + -5r = 0 Combine like terms: 3r + -5r = -2r 2p + 3q + -2r = 0 Solving 2p + 3q + -2r = 0 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3q' to each side of the equation. 2p + 3q + -3q + -2r = 0 + -3q Combine like terms: 3q + -3q = 0 2p + 0 + -2r = 0 + -3q 2p + -2r = 0 + -3q Remove the zero: 2p + -2r = -3q Add '2r' to each side of the equation. 2p + -2r + 2r = -3q + 2r Combine like terms: -2r + 2r = 0 2p + 0 = -3q + 2r 2p = -3q + 2r Divide each side by '2'. p = -1.5q + r Simplifying p = -1.5q + r
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