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Simplifying -6(1 + -2p) + -5(4p + 6) = 1 + p + 7p + -5 (1 * -6 + -2p * -6) + -5(4p + 6) = 1 + p + 7p + -5 (-6 + 12p) + -5(4p + 6) = 1 + p + 7p + -5 Reorder the terms: -6 + 12p + -5(6 + 4p) = 1 + p + 7p + -5 -6 + 12p + (6 * -5 + 4p * -5) = 1 + p + 7p + -5 -6 + 12p + (-30 + -20p) = 1 + p + 7p + -5 Reorder the terms: -6 + -30 + 12p + -20p = 1 + p + 7p + -5 Combine like terms: -6 + -30 = -36 -36 + 12p + -20p = 1 + p + 7p + -5 Combine like terms: 12p + -20p = -8p -36 + -8p = 1 + p + 7p + -5 Reorder the terms: -36 + -8p = 1 + -5 + p + 7p Combine like terms: 1 + -5 = -4 -36 + -8p = -4 + p + 7p Combine like terms: p + 7p = 8p -36 + -8p = -4 + 8p Solving -36 + -8p = -4 + 8p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-8p' to each side of the equation. -36 + -8p + -8p = -4 + 8p + -8p Combine like terms: -8p + -8p = -16p -36 + -16p = -4 + 8p + -8p Combine like terms: 8p + -8p = 0 -36 + -16p = -4 + 0 -36 + -16p = -4 Add '36' to each side of the equation. -36 + 36 + -16p = -4 + 36 Combine like terms: -36 + 36 = 0 0 + -16p = -4 + 36 -16p = -4 + 36 Combine like terms: -4 + 36 = 32 -16p = 32 Divide each side by '-16'. p = -2 Simplifying p = -2
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