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Simplifying (2p + 3)(2p + -3) = (2p + 10)(2p + -10) + -91p Reorder the terms: (3 + 2p)(2p + -3) = (2p + 10)(2p + -10) + -91p Reorder the terms: (3 + 2p)(-3 + 2p) = (2p + 10)(2p + -10) + -91p Multiply (3 + 2p) * (-3 + 2p) (3(-3 + 2p) + 2p * (-3 + 2p)) = (2p + 10)(2p + -10) + -91p ((-3 * 3 + 2p * 3) + 2p * (-3 + 2p)) = (2p + 10)(2p + -10) + -91p ((-9 + 6p) + 2p * (-3 + 2p)) = (2p + 10)(2p + -10) + -91p (-9 + 6p + (-3 * 2p + 2p * 2p)) = (2p + 10)(2p + -10) + -91p (-9 + 6p + (-6p + 4p2)) = (2p + 10)(2p + -10) + -91p Combine like terms: 6p + -6p = 0 (-9 + 0 + 4p2) = (2p + 10)(2p + -10) + -91p (-9 + 4p2) = (2p + 10)(2p + -10) + -91p Reorder the terms: -9 + 4p2 = (10 + 2p)(2p + -10) + -91p Reorder the terms: -9 + 4p2 = (10 + 2p)(-10 + 2p) + -91p Multiply (10 + 2p) * (-10 + 2p) -9 + 4p2 = (10(-10 + 2p) + 2p * (-10 + 2p)) + -91p -9 + 4p2 = ((-10 * 10 + 2p * 10) + 2p * (-10 + 2p)) + -91p -9 + 4p2 = ((-100 + 20p) + 2p * (-10 + 2p)) + -91p -9 + 4p2 = (-100 + 20p + (-10 * 2p + 2p * 2p)) + -91p -9 + 4p2 = (-100 + 20p + (-20p + 4p2)) + -91p Combine like terms: 20p + -20p = 0 -9 + 4p2 = (-100 + 0 + 4p2) + -91p -9 + 4p2 = (-100 + 4p2) + -91p Reorder the terms: -9 + 4p2 = -100 + -91p + 4p2 Add '-4p2' to each side of the equation. -9 + 4p2 + -4p2 = -100 + -91p + 4p2 + -4p2 Combine like terms: 4p2 + -4p2 = 0 -9 + 0 = -100 + -91p + 4p2 + -4p2 -9 = -100 + -91p + 4p2 + -4p2 Combine like terms: 4p2 + -4p2 = 0 -9 = -100 + -91p + 0 -9 = -100 + -91p Solving -9 = -100 + -91p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '91p' to each side of the equation. -9 + 91p = -100 + -91p + 91p Combine like terms: -91p + 91p = 0 -9 + 91p = -100 + 0 -9 + 91p = -100 Add '9' to each side of the equation. -9 + 9 + 91p = -100 + 9 Combine like terms: -9 + 9 = 0 0 + 91p = -100 + 9 91p = -100 + 9 Combine like terms: -100 + 9 = -91 91p = -91 Divide each side by '91'. p = -1 Simplifying p = -1
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