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Simplifying 12p(3p + -4) + 3 = 5 + 4p(9p + -2) Reorder the terms: 12p(-4 + 3p) + 3 = 5 + 4p(9p + -2) (-4 * 12p + 3p * 12p) + 3 = 5 + 4p(9p + -2) (-48p + 36p2) + 3 = 5 + 4p(9p + -2) Reorder the terms: 3 + -48p + 36p2 = 5 + 4p(9p + -2) Reorder the terms: 3 + -48p + 36p2 = 5 + 4p(-2 + 9p) 3 + -48p + 36p2 = 5 + (-2 * 4p + 9p * 4p) 3 + -48p + 36p2 = 5 + (-8p + 36p2) Add '-36p2' to each side of the equation. 3 + -48p + 36p2 + -36p2 = 5 + -8p + 36p2 + -36p2 Combine like terms: 36p2 + -36p2 = 0 3 + -48p + 0 = 5 + -8p + 36p2 + -36p2 3 + -48p = 5 + -8p + 36p2 + -36p2 Combine like terms: 36p2 + -36p2 = 0 3 + -48p = 5 + -8p + 0 3 + -48p = 5 + -8p Solving 3 + -48p = 5 + -8p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '8p' to each side of the equation. 3 + -48p + 8p = 5 + -8p + 8p Combine like terms: -48p + 8p = -40p 3 + -40p = 5 + -8p + 8p Combine like terms: -8p + 8p = 0 3 + -40p = 5 + 0 3 + -40p = 5 Add '-3' to each side of the equation. 3 + -3 + -40p = 5 + -3 Combine like terms: 3 + -3 = 0 0 + -40p = 5 + -3 -40p = 5 + -3 Combine like terms: 5 + -3 = 2 -40p = 2 Divide each side by '-40'. p = -0.05 Simplifying p = -0.05
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