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Simplifying 3p + 4q + -8(3p + -5q + 6r) = 0 3p + 4q + (3p * -8 + -5q * -8 + 6r * -8) = 0 3p + 4q + (-24p + 40q + -48r) = 0 Reorder the terms: 3p + -24p + 4q + 40q + -48r = 0 Combine like terms: 3p + -24p = -21p -21p + 4q + 40q + -48r = 0 Combine like terms: 4q + 40q = 44q -21p + 44q + -48r = 0 Solving -21p + 44q + -48r = 0 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-44q' to each side of the equation. -21p + 44q + -44q + -48r = 0 + -44q Combine like terms: 44q + -44q = 0 -21p + 0 + -48r = 0 + -44q -21p + -48r = 0 + -44q Remove the zero: -21p + -48r = -44q Add '48r' to each side of the equation. -21p + -48r + 48r = -44q + 48r Combine like terms: -48r + 48r = 0 -21p + 0 = -44q + 48r -21p = -44q + 48r Divide each side by '-21'. p = 2.095238095q + -2.285714286r Simplifying p = 2.095238095q + -2.285714286r
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