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Simplifying (3p + -4q + 8r) + -7(-3 + 5q + -3r) = 0 Remove parenthesis around (3p + -4q + 8r) 3p + -4q + 8r + -7(-3 + 5q + -3r) = 0 3p + -4q + 8r + (-3 * -7 + 5q * -7 + -3r * -7) = 0 3p + -4q + 8r + (21 + -35q + 21r) = 0 Reorder the terms: 21 + 3p + -4q + -35q + 8r + 21r = 0 Combine like terms: -4q + -35q = -39q 21 + 3p + -39q + 8r + 21r = 0 Combine like terms: 8r + 21r = 29r 21 + 3p + -39q + 29r = 0 Solving 21 + 3p + -39q + 29r = 0 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + 3p + -39q + -21 + 29r = 0 + -21 Reorder the terms: 21 + -21 + 3p + -39q + 29r = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 3p + -39q + 29r = 0 + -21 3p + -39q + 29r = 0 + -21 Combine like terms: 0 + -21 = -21 3p + -39q + 29r = -21 Add '39q' to each side of the equation. 3p + -39q + 39q + 29r = -21 + 39q Combine like terms: -39q + 39q = 0 3p + 0 + 29r = -21 + 39q 3p + 29r = -21 + 39q Add '-29r' to each side of the equation. 3p + 29r + -29r = -21 + 39q + -29r Combine like terms: 29r + -29r = 0 3p + 0 = -21 + 39q + -29r 3p = -21 + 39q + -29r Divide each side by '3'. p = -7 + 13q + -9.666666667r Simplifying p = -7 + 13q + -9.666666667r
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