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Simplifying -15(3p + -2) + 10(4p + 2) = p + -1(8p + -32) Reorder the terms: -15(-2 + 3p) + 10(4p + 2) = p + -1(8p + -32) (-2 * -15 + 3p * -15) + 10(4p + 2) = p + -1(8p + -32) (30 + -45p) + 10(4p + 2) = p + -1(8p + -32) Reorder the terms: 30 + -45p + 10(2 + 4p) = p + -1(8p + -32) 30 + -45p + (2 * 10 + 4p * 10) = p + -1(8p + -32) 30 + -45p + (20 + 40p) = p + -1(8p + -32) Reorder the terms: 30 + 20 + -45p + 40p = p + -1(8p + -32) Combine like terms: 30 + 20 = 50 50 + -45p + 40p = p + -1(8p + -32) Combine like terms: -45p + 40p = -5p 50 + -5p = p + -1(8p + -32) Reorder the terms: 50 + -5p = p + -1(-32 + 8p) 50 + -5p = p + (-32 * -1 + 8p * -1) 50 + -5p = p + (32 + -8p) Reorder the terms: 50 + -5p = 32 + p + -8p Combine like terms: p + -8p = -7p 50 + -5p = 32 + -7p Solving 50 + -5p = 32 + -7p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '7p' to each side of the equation. 50 + -5p + 7p = 32 + -7p + 7p Combine like terms: -5p + 7p = 2p 50 + 2p = 32 + -7p + 7p Combine like terms: -7p + 7p = 0 50 + 2p = 32 + 0 50 + 2p = 32 Add '-50' to each side of the equation. 50 + -50 + 2p = 32 + -50 Combine like terms: 50 + -50 = 0 0 + 2p = 32 + -50 2p = 32 + -50 Combine like terms: 32 + -50 = -18 2p = -18 Divide each side by '2'. p = -9 Simplifying p = -9
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