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Simplifying 3x2 + 5x + 3(4p + -1) = 0 Reorder the terms: 3x2 + 5x + 3(-1 + 4p) = 0 3x2 + 5x + (-1 * 3 + 4p * 3) = 0 3x2 + 5x + (-3 + 12p) = 0 Reorder the terms: -3 + 12p + 5x + 3x2 = 0 Solving -3 + 12p + 5x + 3x2 = 0 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 12p + 5x + 3 + 3x2 = 0 + 3 Reorder the terms: -3 + 3 + 12p + 5x + 3x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 12p + 5x + 3x2 = 0 + 3 12p + 5x + 3x2 = 0 + 3 Combine like terms: 0 + 3 = 3 12p + 5x + 3x2 = 3 Add '-5x' to each side of the equation. 12p + 5x + -5x + 3x2 = 3 + -5x Combine like terms: 5x + -5x = 0 12p + 0 + 3x2 = 3 + -5x 12p + 3x2 = 3 + -5x Add '-3x2' to each side of the equation. 12p + 3x2 + -3x2 = 3 + -5x + -3x2 Combine like terms: 3x2 + -3x2 = 0 12p + 0 = 3 + -5x + -3x2 12p = 3 + -5x + -3x2 Divide each side by '12'. p = 0.25 + -0.4166666667x + -0.25x2 Simplifying p = 0.25 + -0.4166666667x + -0.25x2
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