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Simplifying -0.09p + -0.05(2 + -3p) = 0.02(p + -3) + -0.12 -0.09p + (2 * -0.05 + -3p * -0.05) = 0.02(p + -3) + -0.12 -0.09p + (-0.1 + 0.15p) = 0.02(p + -3) + -0.12 Reorder the terms: -0.1 + -0.09p + 0.15p = 0.02(p + -3) + -0.12 Combine like terms: -0.09p + 0.15p = 0.06p -0.1 + 0.06p = 0.02(p + -3) + -0.12 Reorder the terms: -0.1 + 0.06p = 0.02(-3 + p) + -0.12 -0.1 + 0.06p = (-3 * 0.02 + p * 0.02) + -0.12 -0.1 + 0.06p = (-0.06 + 0.02p) + -0.12 Reorder the terms: -0.1 + 0.06p = -0.06 + -0.12 + 0.02p Combine like terms: -0.06 + -0.12 = -0.18 -0.1 + 0.06p = -0.18 + 0.02p Solving -0.1 + 0.06p = -0.18 + 0.02p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.02p' to each side of the equation. -0.1 + 0.06p + -0.02p = -0.18 + 0.02p + -0.02p Combine like terms: 0.06p + -0.02p = 0.04p -0.1 + 0.04p = -0.18 + 0.02p + -0.02p Combine like terms: 0.02p + -0.02p = 0.00 -0.1 + 0.04p = -0.18 + 0.00 -0.1 + 0.04p = -0.18 Add '0.1' to each side of the equation. -0.1 + 0.1 + 0.04p = -0.18 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + 0.04p = -0.18 + 0.1 0.04p = -0.18 + 0.1 Combine like terms: -0.18 + 0.1 = -0.08 0.04p = -0.08 Divide each side by '0.04'. p = -2 Simplifying p = -2
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