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Simplifying (x + -2)(x + -4) * x(x + 2)(x + 3)(x + 6) + 100 = 0 Reorder the terms: (-2 + x)(x + -4) * x(x + 2)(x + 3)(x + 6) + 100 = 0 Reorder the terms: (-2 + x)(-4 + x) * x(x + 2)(x + 3)(x + 6) + 100 = 0 Reorder the terms: (-2 + x)(-4 + x) * x(2 + x)(x + 3)(x + 6) + 100 = 0 Reorder the terms: (-2 + x)(-4 + x) * x(2 + x)(3 + x)(x + 6) + 100 = 0 Reorder the terms: (-2 + x)(-4 + x) * x(2 + x)(3 + x)(6 + x) + 100 = 0 Reorder the terms for easier multiplication: x(-2 + x)(-4 + x)(2 + x)(3 + x)(6 + x) + 100 = 0 Multiply (-2 + x) * (-4 + x) x(-2(-4 + x) + x(-4 + x))(2 + x)(3 + x)(6 + x) + 100 = 0 x((-4 * -2 + x * -2) + x(-4 + x))(2 + x)(3 + x)(6 + x) + 100 = 0 x((8 + -2x) + x(-4 + x))(2 + x)(3 + x)(6 + x) + 100 = 0 x(8 + -2x + (-4 * x + x * x))(2 + x)(3 + x)(6 + x) + 100 = 0 x(8 + -2x + (-4x + x2))(2 + x)(3 + x)(6 + x) + 100 = 0 Combine like terms: -2x + -4x = -6x x(8 + -6x + x2)(2 + x)(3 + x)(6 + x) + 100 = 0 Multiply (8 + -6x + x2) * (2 + x) x(8(2 + x) + -6x * (2 + x) + x2(2 + x))(3 + x)(6 + x) + 100 = 0 x((2 * 8 + x * 8) + -6x * (2 + x) + x2(2 + x))(3 + x)(6 + x) + 100 = 0 x((16 + 8x) + -6x * (2 + x) + x2(2 + x))(3 + x)(6 + x) + 100 = 0 x(16 + 8x + (2 * -6x + x * -6x) + x2(2 + x))(3 + x)(6 + x) + 100 = 0 x(16 + 8x + (-12x + -6x2) + x2(2 + x))(3 + x)(6 + x) + 100 = 0 x(16 + 8x + -12x + -6x2 + (2 * x2 + x * x2))(3 + x)(6 + x) + 100 = 0 x(16 + 8x + -12x + -6x2 + (2x2 + x3))(3 + x)(6 + x) + 100 = 0 Combine like terms: 8x + -12x = -4x x(16 + -4x + -6x2 + 2x2 + x3)(3 + x)(6 + x) + 100 = 0 Combine like terms: -6x2 + 2x2 = -4x2 x(16 + -4x + -4x2 + x3)(3 + x)(6 + x) + 100 = 0 Multiply (16 + -4x + -4x2 + x3) * (3 + x) x(16(3 + x) + -4x * (3 + x) + -4x2 * (3 + x) + x3(3 + x))(6 + x) + 100 = 0 x((3 * 16 + x * 16) + -4x * (3 + x) + -4x2 * (3 + x) + x3(3 + x))(6 + x) + 100 = 0 x((48 + 16x) + -4x * (3 + x) + -4x2 * (3 + x) + x3(3 + x))(6 + x) + 100 = 0 x(48 + 16x + (3 * -4x + x * -4x) + -4x2 * (3 + x) + x3(3 + x))(6 + x) + 100 = 0 x(48 + 16x + (-12x + -4x2) + -4x2 * (3 + x) + x3(3 + x))(6 + x) + 100 = 0 x(48 + 16x + -12x + -4x2 + (3 * -4x2 + x * -4x2) + x3(3 + x))(6 + x) + 100 = 0 x(48 + 16x + -12x + -4x2 + (-12x2 + -4x3) + x3(3 + x))(6 + x) + 100 = 0 x(48 + 16x + -12x + -4x2 + -12x2 + -4x3 + (3 * x3 + x * x3))(6 + x) + 100 = 0 x(48 + 16x + -12x + -4x2 + -12x2 + -4x3 + (3x3 + x4))(6 + x) + 100 = 0 Combine like terms: 16x + -12x = 4x x(48 + 4x + -4x2 + -12x2 + -4x3 + 3x3 + x4)(6 + x) + 100 = 0 Combine like terms: -4x2 + -12x2 = -16x2 x(48 + 4x + -16x2 + -4x3 + 3x3 + x4)(6 + x) + 100 = 0 Combine like terms: -4x3 + 3x3 = -1x3 x(48 + 4x + -16x2 + -1x3 + x4)(6 + x) + 100 = 0 Multiply (48 + 4x + -16x2 + -1x3 + x4) * (6 + x) x(48(6 + x) + 4x * (6 + x) + -16x2 * (6 + x) + -1x3 * (6 + x) + x4(6 + x)) + 100 = 0 x((6 * 48 + x * 48) + 4x * (6 + x) + -16x2 * (6 + x) + -1x3 * (6 + x) + x4(6 + x)) + 100 = 0 x((288 + 48x) + 4x * (6 + x) + -16x2 * (6 + x) + -1x3 * (6 + x) + x4(6 + x)) + 100 = 0 x(288 + 48x + (6 * 4x + x * 4x) + -16x2 * (6 + x) + -1x3 * (6 + x) + x4(6 + x)) + 100 = 0 x(288 + 48x + (24x + 4x2) + -16x2 * (6 + x) + -1x3 * (6 + x) + x4(6 + x)) + 100 = 0 x(288 + 48x + 24x + 4x2 + (6 * -16x2 + x * -16x2) + -1x3 * (6 + x) + x4(6 + x)) + 100 = 0 x(288 + 48x + 24x + 4x2 + (-96x2 + -16x3) + -1x3 * (6 + x) + x4(6 + x)) + 100 = 0 x(288 + 48x + 24x + 4x2 + -96x2 + -16x3 + (6 * -1x3 + x * -1x3) + x4(6 + x)) + 100 = 0 x(288 + 48x + 24x + 4x2 + -96x2 + -16x3 + (-6x3 + -1x4) + x4(6 + x)) + 100 = 0 x(288 + 48x + 24x + 4x2 + -96x2 + -16x3 + -6x3 + -1x4 + (6 * x4 + x * x4)) + 100 = 0 x(288 + 48x + 24x + 4x2 + -96x2 + -16x3 + -6x3 + -1x4 + (6x4 + x5)) + 100 = 0 Combine like terms: 48x + 24x = 72x x(288 + 72x + 4x2 + -96x2 + -16x3 + -6x3 + -1x4 + 6x4 + x5) + 100 = 0 Combine like terms: 4x2 + -96x2 = -92x2 x(288 + 72x + -92x2 + -16x3 + -6x3 + -1x4 + 6x4 + x5) + 100 = 0 Combine like terms: -16x3 + -6x3 = -22x3 x(288 + 72x + -92x2 + -22x3 + -1x4 + 6x4 + x5) + 100 = 0 Combine like terms: -1x4 + 6x4 = 5x4 x(288 + 72x + -92x2 + -22x3 + 5x4 + x5) + 100 = 0 (288 * x + 72x * x + -92x2 * x + -22x3 * x + 5x4 * x + x5 * x) + 100 = 0 (288x + 72x2 + -92x3 + -22x4 + 5x5 + x6) + 100 = 0 Reorder the terms: 100 + 288x + 72x2 + -92x3 + -22x4 + 5x5 + x6 = 0 Solving 100 + 288x + 72x2 + -92x3 + -22x4 + 5x5 + x6 = 0 Solving for variable 'x'. The solution to this equation could not be determined.
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