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Simplifying 0.02p + -0.04(3 + -2p) = 0.05(p + -6) + -0.42 0.02p + (3 * -0.04 + -2p * -0.04) = 0.05(p + -6) + -0.42 0.02p + (-0.12 + 0.08p) = 0.05(p + -6) + -0.42 Reorder the terms: -0.12 + 0.02p + 0.08p = 0.05(p + -6) + -0.42 Combine like terms: 0.02p + 0.08p = 0.1p -0.12 + 0.1p = 0.05(p + -6) + -0.42 Reorder the terms: -0.12 + 0.1p = 0.05(-6 + p) + -0.42 -0.12 + 0.1p = (-6 * 0.05 + p * 0.05) + -0.42 -0.12 + 0.1p = (-0.3 + 0.05p) + -0.42 Reorder the terms: -0.12 + 0.1p = -0.3 + -0.42 + 0.05p Combine like terms: -0.3 + -0.42 = -0.72 -0.12 + 0.1p = -0.72 + 0.05p Solving -0.12 + 0.1p = -0.72 + 0.05p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.05p' to each side of the equation. -0.12 + 0.1p + -0.05p = -0.72 + 0.05p + -0.05p Combine like terms: 0.1p + -0.05p = 0.05p -0.12 + 0.05p = -0.72 + 0.05p + -0.05p Combine like terms: 0.05p + -0.05p = 0.00 -0.12 + 0.05p = -0.72 + 0.00 -0.12 + 0.05p = -0.72 Add '0.12' to each side of the equation. -0.12 + 0.12 + 0.05p = -0.72 + 0.12 Combine like terms: -0.12 + 0.12 = 0.00 0.00 + 0.05p = -0.72 + 0.12 0.05p = -0.72 + 0.12 Combine like terms: -0.72 + 0.12 = -0.6 0.05p = -0.6 Divide each side by '0.05'. p = -12 Simplifying p = -12
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