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Simplifying -20p(3p + -2)(3p + -2) + -20(3p + -2) * p + -5p = -45p(2p + -1)(2p + -1) Reorder the terms: -20p(-2 + 3p)(3p + -2) + -20(3p + -2) * p + -5p = -45p(2p + -1)(2p + -1) Reorder the terms: -20p(-2 + 3p)(-2 + 3p) + -20(3p + -2) * p + -5p = -45p(2p + -1)(2p + -1) Multiply (-2 + 3p) * (-2 + 3p) -20p(-2(-2 + 3p) + 3p * (-2 + 3p)) + -20(3p + -2) * p + -5p = -45p(2p + -1)(2p + -1) -20p((-2 * -2 + 3p * -2) + 3p * (-2 + 3p)) + -20(3p + -2) * p + -5p = -45p(2p + -1)(2p + -1) -20p((4 + -6p) + 3p * (-2 + 3p)) + -20(3p + -2) * p + -5p = -45p(2p + -1)(2p + -1) -20p(4 + -6p + (-2 * 3p + 3p * 3p)) + -20(3p + -2) * p + -5p = -45p(2p + -1)(2p + -1) -20p(4 + -6p + (-6p + 9p2)) + -20(3p + -2) * p + -5p = -45p(2p + -1)(2p + -1) Combine like terms: -6p + -6p = -12p -20p(4 + -12p + 9p2) + -20(3p + -2) * p + -5p = -45p(2p + -1)(2p + -1) (4 * -20p + -12p * -20p + 9p2 * -20p) + -20(3p + -2) * p + -5p = -45p(2p + -1)(2p + -1) (-80p + 240p2 + -180p3) + -20(3p + -2) * p + -5p = -45p(2p + -1)(2p + -1) Reorder the terms: -80p + 240p2 + -180p3 + -20(-2 + 3p) * p + -5p = -45p(2p + -1)(2p + -1) Reorder the terms for easier multiplication: -80p + 240p2 + -180p3 + -20p(-2 + 3p) + -5p = -45p(2p + -1)(2p + -1) -80p + 240p2 + -180p3 + (-2 * -20p + 3p * -20p) + -5p = -45p(2p + -1)(2p + -1) -80p + 240p2 + -180p3 + (40p + -60p2) + -5p = -45p(2p + -1)(2p + -1) Reorder the terms: -80p + 40p + -5p + 240p2 + -60p2 + -180p3 = -45p(2p + -1)(2p + -1) Combine like terms: -80p + 40p = -40p -40p + -5p + 240p2 + -60p2 + -180p3 = -45p(2p + -1)(2p + -1) Combine like terms: -40p + -5p = -45p -45p + 240p2 + -60p2 + -180p3 = -45p(2p + -1)(2p + -1) Combine like terms: 240p2 + -60p2 = 180p2 -45p + 180p2 + -180p3 = -45p(2p + -1)(2p + -1) Reorder the terms: -45p + 180p2 + -180p3 = -45p(-1 + 2p)(2p + -1) Reorder the terms: -45p + 180p2 + -180p3 = -45p(-1 + 2p)(-1 + 2p) Multiply (-1 + 2p) * (-1 + 2p) -45p + 180p2 + -180p3 = -45p(-1(-1 + 2p) + 2p * (-1 + 2p)) -45p + 180p2 + -180p3 = -45p((-1 * -1 + 2p * -1) + 2p * (-1 + 2p)) -45p + 180p2 + -180p3 = -45p((1 + -2p) + 2p * (-1 + 2p)) -45p + 180p2 + -180p3 = -45p(1 + -2p + (-1 * 2p + 2p * 2p)) -45p + 180p2 + -180p3 = -45p(1 + -2p + (-2p + 4p2)) Combine like terms: -2p + -2p = -4p -45p + 180p2 + -180p3 = -45p(1 + -4p + 4p2) -45p + 180p2 + -180p3 = (1 * -45p + -4p * -45p + 4p2 * -45p) -45p + 180p2 + -180p3 = (-45p + 180p2 + -180p3) Add '45p' to each side of the equation. -45p + 180p2 + 45p + -180p3 = -45p + 180p2 + 45p + -180p3 Reorder the terms: -45p + 45p + 180p2 + -180p3 = -45p + 180p2 + 45p + -180p3 Combine like terms: -45p + 45p = 0 0 + 180p2 + -180p3 = -45p + 180p2 + 45p + -180p3 180p2 + -180p3 = -45p + 180p2 + 45p + -180p3 Reorder the terms: 180p2 + -180p3 = -45p + 45p + 180p2 + -180p3 Combine like terms: -45p + 45p = 0 180p2 + -180p3 = 0 + 180p2 + -180p3 180p2 + -180p3 = 180p2 + -180p3 Add '-180p2' to each side of the equation. 180p2 + -180p2 + -180p3 = 180p2 + -180p2 + -180p3 Combine like terms: 180p2 + -180p2 = 0 0 + -180p3 = 180p2 + -180p2 + -180p3 -180p3 = 180p2 + -180p2 + -180p3 Combine like terms: 180p2 + -180p2 = 0 -180p3 = 0 + -180p3 -180p3 = -180p3 Add '180p3' to each side of the equation. -180p3 + 180p3 = -180p3 + 180p3 Combine like terms: -180p3 + 180p3 = 0 0 = -180p3 + 180p3 Combine like terms: -180p3 + 180p3 = 0 0 = 0 Solving 0 = 0 Couldn't find a variable to solve for. This equation is an identity, all real numbers are solutions.
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