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Simplifying -12p + -5(6 + -4p) = 3(p + -3) + -31 -12p + (6 * -5 + -4p * -5) = 3(p + -3) + -31 -12p + (-30 + 20p) = 3(p + -3) + -31 Reorder the terms: -30 + -12p + 20p = 3(p + -3) + -31 Combine like terms: -12p + 20p = 8p -30 + 8p = 3(p + -3) + -31 Reorder the terms: -30 + 8p = 3(-3 + p) + -31 -30 + 8p = (-3 * 3 + p * 3) + -31 -30 + 8p = (-9 + 3p) + -31 Reorder the terms: -30 + 8p = -9 + -31 + 3p Combine like terms: -9 + -31 = -40 -30 + 8p = -40 + 3p Solving -30 + 8p = -40 + 3p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3p' to each side of the equation. -30 + 8p + -3p = -40 + 3p + -3p Combine like terms: 8p + -3p = 5p -30 + 5p = -40 + 3p + -3p Combine like terms: 3p + -3p = 0 -30 + 5p = -40 + 0 -30 + 5p = -40 Add '30' to each side of the equation. -30 + 30 + 5p = -40 + 30 Combine like terms: -30 + 30 = 0 0 + 5p = -40 + 30 5p = -40 + 30 Combine like terms: -40 + 30 = -10 5p = -10 Divide each side by '5'. p = -2 Simplifying p = -2
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