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Simplifying 4(3p + 2) + -5(6p + -1) = 2(p + -8) + -6(7p + -4) Reorder the terms: 4(2 + 3p) + -5(6p + -1) = 2(p + -8) + -6(7p + -4) (2 * 4 + 3p * 4) + -5(6p + -1) = 2(p + -8) + -6(7p + -4) (8 + 12p) + -5(6p + -1) = 2(p + -8) + -6(7p + -4) Reorder the terms: 8 + 12p + -5(-1 + 6p) = 2(p + -8) + -6(7p + -4) 8 + 12p + (-1 * -5 + 6p * -5) = 2(p + -8) + -6(7p + -4) 8 + 12p + (5 + -30p) = 2(p + -8) + -6(7p + -4) Reorder the terms: 8 + 5 + 12p + -30p = 2(p + -8) + -6(7p + -4) Combine like terms: 8 + 5 = 13 13 + 12p + -30p = 2(p + -8) + -6(7p + -4) Combine like terms: 12p + -30p = -18p 13 + -18p = 2(p + -8) + -6(7p + -4) Reorder the terms: 13 + -18p = 2(-8 + p) + -6(7p + -4) 13 + -18p = (-8 * 2 + p * 2) + -6(7p + -4) 13 + -18p = (-16 + 2p) + -6(7p + -4) Reorder the terms: 13 + -18p = -16 + 2p + -6(-4 + 7p) 13 + -18p = -16 + 2p + (-4 * -6 + 7p * -6) 13 + -18p = -16 + 2p + (24 + -42p) Reorder the terms: 13 + -18p = -16 + 24 + 2p + -42p Combine like terms: -16 + 24 = 8 13 + -18p = 8 + 2p + -42p Combine like terms: 2p + -42p = -40p 13 + -18p = 8 + -40p Solving 13 + -18p = 8 + -40p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '40p' to each side of the equation. 13 + -18p + 40p = 8 + -40p + 40p Combine like terms: -18p + 40p = 22p 13 + 22p = 8 + -40p + 40p Combine like terms: -40p + 40p = 0 13 + 22p = 8 + 0 13 + 22p = 8 Add '-13' to each side of the equation. 13 + -13 + 22p = 8 + -13 Combine like terms: 13 + -13 = 0 0 + 22p = 8 + -13 22p = 8 + -13 Combine like terms: 8 + -13 = -5 22p = -5 Divide each side by '22'. p = -0.2272727273 Simplifying p = -0.2272727273
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