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Simplifying (3p + 1) + 6(p + -8) + -1(p + 2) = 0 Reorder the terms: (1 + 3p) + 6(p + -8) + -1(p + 2) = 0 Remove parenthesis around (1 + 3p) 1 + 3p + 6(p + -8) + -1(p + 2) = 0 Reorder the terms: 1 + 3p + 6(-8 + p) + -1(p + 2) = 0 1 + 3p + (-8 * 6 + p * 6) + -1(p + 2) = 0 1 + 3p + (-48 + 6p) + -1(p + 2) = 0 Reorder the terms: 1 + 3p + -48 + 6p + -1(2 + p) = 0 1 + 3p + -48 + 6p + (2 * -1 + p * -1) = 0 1 + 3p + -48 + 6p + (-2 + -1p) = 0 Reorder the terms: 1 + -48 + -2 + 3p + 6p + -1p = 0 Combine like terms: 1 + -48 = -47 -47 + -2 + 3p + 6p + -1p = 0 Combine like terms: -47 + -2 = -49 -49 + 3p + 6p + -1p = 0 Combine like terms: 3p + 6p = 9p -49 + 9p + -1p = 0 Combine like terms: 9p + -1p = 8p -49 + 8p = 0 Solving -49 + 8p = 0 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '49' to each side of the equation. -49 + 49 + 8p = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 8p = 0 + 49 8p = 0 + 49 Combine like terms: 0 + 49 = 49 8p = 49 Divide each side by '8'. p = 6.125 Simplifying p = 6.125
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