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Simplifying 4p + 5(3p + -2) + -4(3p + 6) + 2(4p + -6) = 0 Reorder the terms: 4p + 5(-2 + 3p) + -4(3p + 6) + 2(4p + -6) = 0 4p + (-2 * 5 + 3p * 5) + -4(3p + 6) + 2(4p + -6) = 0 4p + (-10 + 15p) + -4(3p + 6) + 2(4p + -6) = 0 Reorder the terms: 4p + -10 + 15p + -4(6 + 3p) + 2(4p + -6) = 0 4p + -10 + 15p + (6 * -4 + 3p * -4) + 2(4p + -6) = 0 4p + -10 + 15p + (-24 + -12p) + 2(4p + -6) = 0 Reorder the terms: 4p + -10 + 15p + -24 + -12p + 2(-6 + 4p) = 0 4p + -10 + 15p + -24 + -12p + (-6 * 2 + 4p * 2) = 0 4p + -10 + 15p + -24 + -12p + (-12 + 8p) = 0 Reorder the terms: -10 + -24 + -12 + 4p + 15p + -12p + 8p = 0 Combine like terms: -10 + -24 = -34 -34 + -12 + 4p + 15p + -12p + 8p = 0 Combine like terms: -34 + -12 = -46 -46 + 4p + 15p + -12p + 8p = 0 Combine like terms: 4p + 15p = 19p -46 + 19p + -12p + 8p = 0 Combine like terms: 19p + -12p = 7p -46 + 7p + 8p = 0 Combine like terms: 7p + 8p = 15p -46 + 15p = 0 Solving -46 + 15p = 0 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '46' to each side of the equation. -46 + 46 + 15p = 0 + 46 Combine like terms: -46 + 46 = 0 0 + 15p = 0 + 46 15p = 0 + 46 Combine like terms: 0 + 46 = 46 15p = 46 Divide each side by '15'. p = 3.066666667 Simplifying p = 3.066666667
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