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Simplifying F(x) = (2x + 3)(2x + -1)(x + 2)(4x + -3) Multiply F * x xF = (2x + 3)(2x + -1)(x + 2)(4x + -3) Reorder the terms: xF = (3 + 2x)(2x + -1)(x + 2)(4x + -3) Reorder the terms: xF = (3 + 2x)(-1 + 2x)(x + 2)(4x + -3) Reorder the terms: xF = (3 + 2x)(-1 + 2x)(2 + x)(4x + -3) Reorder the terms: xF = (3 + 2x)(-1 + 2x)(2 + x)(-3 + 4x) Multiply (3 + 2x) * (-1 + 2x) xF = (3(-1 + 2x) + 2x * (-1 + 2x))(2 + x)(-3 + 4x) xF = ((-1 * 3 + 2x * 3) + 2x * (-1 + 2x))(2 + x)(-3 + 4x) xF = ((-3 + 6x) + 2x * (-1 + 2x))(2 + x)(-3 + 4x) xF = (-3 + 6x + (-1 * 2x + 2x * 2x))(2 + x)(-3 + 4x) xF = (-3 + 6x + (-2x + 4x2))(2 + x)(-3 + 4x) Combine like terms: 6x + -2x = 4x xF = (-3 + 4x + 4x2)(2 + x)(-3 + 4x) Multiply (-3 + 4x + 4x2) * (2 + x) xF = (-3(2 + x) + 4x * (2 + x) + 4x2 * (2 + x))(-3 + 4x) xF = ((2 * -3 + x * -3) + 4x * (2 + x) + 4x2 * (2 + x))(-3 + 4x) xF = ((-6 + -3x) + 4x * (2 + x) + 4x2 * (2 + x))(-3 + 4x) xF = (-6 + -3x + (2 * 4x + x * 4x) + 4x2 * (2 + x))(-3 + 4x) xF = (-6 + -3x + (8x + 4x2) + 4x2 * (2 + x))(-3 + 4x) xF = (-6 + -3x + 8x + 4x2 + (2 * 4x2 + x * 4x2))(-3 + 4x) xF = (-6 + -3x + 8x + 4x2 + (8x2 + 4x3))(-3 + 4x) Combine like terms: -3x + 8x = 5x xF = (-6 + 5x + 4x2 + 8x2 + 4x3)(-3 + 4x) Combine like terms: 4x2 + 8x2 = 12x2 xF = (-6 + 5x + 12x2 + 4x3)(-3 + 4x) Multiply (-6 + 5x + 12x2 + 4x3) * (-3 + 4x) xF = (-6(-3 + 4x) + 5x * (-3 + 4x) + 12x2 * (-3 + 4x) + 4x3 * (-3 + 4x)) xF = ((-3 * -6 + 4x * -6) + 5x * (-3 + 4x) + 12x2 * (-3 + 4x) + 4x3 * (-3 + 4x)) xF = ((18 + -24x) + 5x * (-3 + 4x) + 12x2 * (-3 + 4x) + 4x3 * (-3 + 4x)) xF = (18 + -24x + (-3 * 5x + 4x * 5x) + 12x2 * (-3 + 4x) + 4x3 * (-3 + 4x)) xF = (18 + -24x + (-15x + 20x2) + 12x2 * (-3 + 4x) + 4x3 * (-3 + 4x)) xF = (18 + -24x + -15x + 20x2 + (-3 * 12x2 + 4x * 12x2) + 4x3 * (-3 + 4x)) xF = (18 + -24x + -15x + 20x2 + (-36x2 + 48x3) + 4x3 * (-3 + 4x)) xF = (18 + -24x + -15x + 20x2 + -36x2 + 48x3 + (-3 * 4x3 + 4x * 4x3)) xF = (18 + -24x + -15x + 20x2 + -36x2 + 48x3 + (-12x3 + 16x4)) Combine like terms: -24x + -15x = -39x xF = (18 + -39x + 20x2 + -36x2 + 48x3 + -12x3 + 16x4) Combine like terms: 20x2 + -36x2 = -16x2 xF = (18 + -39x + -16x2 + 48x3 + -12x3 + 16x4) Combine like terms: 48x3 + -12x3 = 36x3 xF = (18 + -39x + -16x2 + 36x3 + 16x4) Solving xF = 18 + -39x + -16x2 + 36x3 + 16x4 Solving for variable 'x'. Reorder the terms: -18 + 39x + xF + 16x2 + -36x3 + -16x4 = 18 + -39x + -16x2 + 36x3 + 16x4 + -18 + 39x + 16x2 + -36x3 + -16x4 Reorder the terms: -18 + 39x + xF + 16x2 + -36x3 + -16x4 = 18 + -18 + -39x + 39x + -16x2 + 16x2 + 36x3 + -36x3 + 16x4 + -16x4 Combine like terms: 18 + -18 = 0 -18 + 39x + xF + 16x2 + -36x3 + -16x4 = 0 + -39x + 39x + -16x2 + 16x2 + 36x3 + -36x3 + 16x4 + -16x4 -18 + 39x + xF + 16x2 + -36x3 + -16x4 = -39x + 39x + -16x2 + 16x2 + 36x3 + -36x3 + 16x4 + -16x4 Combine like terms: -39x + 39x = 0 -18 + 39x + xF + 16x2 + -36x3 + -16x4 = 0 + -16x2 + 16x2 + 36x3 + -36x3 + 16x4 + -16x4 -18 + 39x + xF + 16x2 + -36x3 + -16x4 = -16x2 + 16x2 + 36x3 + -36x3 + 16x4 + -16x4 Combine like terms: -16x2 + 16x2 = 0 -18 + 39x + xF + 16x2 + -36x3 + -16x4 = 0 + 36x3 + -36x3 + 16x4 + -16x4 -18 + 39x + xF + 16x2 + -36x3 + -16x4 = 36x3 + -36x3 + 16x4 + -16x4 Combine like terms: 36x3 + -36x3 = 0 -18 + 39x + xF + 16x2 + -36x3 + -16x4 = 0 + 16x4 + -16x4 -18 + 39x + xF + 16x2 + -36x3 + -16x4 = 16x4 + -16x4 Combine like terms: 16x4 + -16x4 = 0 -18 + 39x + xF + 16x2 + -36x3 + -16x4 = 0 The solution to this equation could not be determined.
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