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Simplifying 0 = ((x + 7)(x + 8)(x + 3)(x + 5)(x + 9)(x + 10)) Reorder the terms: 0 = ((7 + x)(x + 8)(x + 3)(x + 5)(x + 9)(x + 10)) Reorder the terms: 0 = ((7 + x)(8 + x)(x + 3)(x + 5)(x + 9)(x + 10)) Reorder the terms: 0 = ((7 + x)(8 + x)(3 + x)(x + 5)(x + 9)(x + 10)) Reorder the terms: 0 = ((7 + x)(8 + x)(3 + x)(5 + x)(x + 9)(x + 10)) Reorder the terms: 0 = ((7 + x)(8 + x)(3 + x)(5 + x)(9 + x)(x + 10)) Reorder the terms: 0 = ((7 + x)(8 + x)(3 + x)(5 + x)(9 + x)(10 + x)) Multiply (7 + x) * (8 + x) 0 = ((7(8 + x) + x(8 + x))(3 + x)(5 + x)(9 + x)(10 + x)) 0 = (((8 * 7 + x * 7) + x(8 + x))(3 + x)(5 + x)(9 + x)(10 + x)) 0 = (((56 + 7x) + x(8 + x))(3 + x)(5 + x)(9 + x)(10 + x)) 0 = ((56 + 7x + (8 * x + x * x))(3 + x)(5 + x)(9 + x)(10 + x)) 0 = ((56 + 7x + (8x + x2))(3 + x)(5 + x)(9 + x)(10 + x)) Combine like terms: 7x + 8x = 15x 0 = ((56 + 15x + x2)(3 + x)(5 + x)(9 + x)(10 + x)) Multiply (56 + 15x + x2) * (3 + x) 0 = ((56(3 + x) + 15x * (3 + x) + x2(3 + x))(5 + x)(9 + x)(10 + x)) 0 = (((3 * 56 + x * 56) + 15x * (3 + x) + x2(3 + x))(5 + x)(9 + x)(10 + x)) 0 = (((168 + 56x) + 15x * (3 + x) + x2(3 + x))(5 + x)(9 + x)(10 + x)) 0 = ((168 + 56x + (3 * 15x + x * 15x) + x2(3 + x))(5 + x)(9 + x)(10 + x)) 0 = ((168 + 56x + (45x + 15x2) + x2(3 + x))(5 + x)(9 + x)(10 + x)) 0 = ((168 + 56x + 45x + 15x2 + (3 * x2 + x * x2))(5 + x)(9 + x)(10 + x)) 0 = ((168 + 56x + 45x + 15x2 + (3x2 + x3))(5 + x)(9 + x)(10 + x)) Combine like terms: 56x + 45x = 101x 0 = ((168 + 101x + 15x2 + 3x2 + x3)(5 + x)(9 + x)(10 + x)) Combine like terms: 15x2 + 3x2 = 18x2 0 = ((168 + 101x + 18x2 + x3)(5 + x)(9 + x)(10 + x)) Multiply (168 + 101x + 18x2 + x3) * (5 + x) 0 = ((168(5 + x) + 101x * (5 + x) + 18x2 * (5 + x) + x3(5 + x))(9 + x)(10 + x)) 0 = (((5 * 168 + x * 168) + 101x * (5 + x) + 18x2 * (5 + x) + x3(5 + x))(9 + x)(10 + x)) 0 = (((840 + 168x) + 101x * (5 + x) + 18x2 * (5 + x) + x3(5 + x))(9 + x)(10 + x)) 0 = ((840 + 168x + (5 * 101x + x * 101x) + 18x2 * (5 + x) + x3(5 + x))(9 + x)(10 + x)) 0 = ((840 + 168x + (505x + 101x2) + 18x2 * (5 + x) + x3(5 + x))(9 + x)(10 + x)) 0 = ((840 + 168x + 505x + 101x2 + (5 * 18x2 + x * 18x2) + x3(5 + x))(9 + x)(10 + x)) 0 = ((840 + 168x + 505x + 101x2 + (90x2 + 18x3) + x3(5 + x))(9 + x)(10 + x)) 0 = ((840 + 168x + 505x + 101x2 + 90x2 + 18x3 + (5 * x3 + x * x3))(9 + x)(10 + x)) 0 = ((840 + 168x + 505x + 101x2 + 90x2 + 18x3 + (5x3 + x4))(9 + x)(10 + x)) Combine like terms: 168x + 505x = 673x 0 = ((840 + 673x + 101x2 + 90x2 + 18x3 + 5x3 + x4)(9 + x)(10 + x)) Combine like terms: 101x2 + 90x2 = 191x2 0 = ((840 + 673x + 191x2 + 18x3 + 5x3 + x4)(9 + x)(10 + x)) Combine like terms: 18x3 + 5x3 = 23x3 0 = ((840 + 673x + 191x2 + 23x3 + x4)(9 + x)(10 + x)) Multiply (840 + 673x + 191x2 + 23x3 + x4) * (9 + x) 0 = ((840(9 + x) + 673x * (9 + x) + 191x2 * (9 + x) + 23x3 * (9 + x) + x4(9 + x))(10 + x)) 0 = (((9 * 840 + x * 840) + 673x * (9 + x) + 191x2 * (9 + x) + 23x3 * (9 + x) + x4(9 + x))(10 + x)) 0 = (((7560 + 840x) + 673x * (9 + x) + 191x2 * (9 + x) + 23x3 * (9 + x) + x4(9 + x))(10 + x)) 0 = ((7560 + 840x + (9 * 673x + x * 673x) + 191x2 * (9 + x) + 23x3 * (9 + x) + x4(9 + x))(10 + x)) 0 = ((7560 + 840x + (6057x + 673x2) + 191x2 * (9 + x) + 23x3 * (9 + x) + x4(9 + x))(10 + x)) 0 = ((7560 + 840x + 6057x + 673x2 + (9 * 191x2 + x * 191x2) + 23x3 * (9 + x) + x4(9 + x))(10 + x)) 0 = ((7560 + 840x + 6057x + 673x2 + (1719x2 + 191x3) + 23x3 * (9 + x) + x4(9 + x))(10 + x)) 0 = ((7560 + 840x + 6057x + 673x2 + 1719x2 + 191x3 + (9 * 23x3 + x * 23x3) + x4(9 + x))(10 + x)) 0 = ((7560 + 840x + 6057x + 673x2 + 1719x2 + 191x3 + (207x3 + 23x4) + x4(9 + x))(10 + x)) 0 = ((7560 + 840x + 6057x + 673x2 + 1719x2 + 191x3 + 207x3 + 23x4 + (9 * x4 + x * x4))(10 + x)) 0 = ((7560 + 840x + 6057x + 673x2 + 1719x2 + 191x3 + 207x3 + 23x4 + (9x4 + x5))(10 + x)) Combine like terms: 840x + 6057x = 6897x 0 = ((7560 + 6897x + 673x2 + 1719x2 + 191x3 + 207x3 + 23x4 + 9x4 + x5)(10 + x)) Combine like terms: 673x2 + 1719x2 = 2392x2 0 = ((7560 + 6897x + 2392x2 + 191x3 + 207x3 + 23x4 + 9x4 + x5)(10 + x)) Combine like terms: 191x3 + 207x3 = 398x3 0 = ((7560 + 6897x + 2392x2 + 398x3 + 23x4 + 9x4 + x5)(10 + x)) Combine like terms: 23x4 + 9x4 = 32x4 0 = ((7560 + 6897x + 2392x2 + 398x3 + 32x4 + x5)(10 + x)) Multiply (7560 + 6897x + 2392x2 + 398x3 + 32x4 + x5) * (10 + x) 0 = ((7560(10 + x) + 6897x * (10 + x) + 2392x2 * (10 + x) + 398x3 * (10 + x) + 32x4 * (10 + x) + x5(10 + x))) 0 = (((10 * 7560 + x * 7560) + 6897x * (10 + x) + 2392x2 * (10 + x) + 398x3 * (10 + x) + 32x4 * (10 + x) + x5(10 + x))) 0 = (((75600 + 7560x) + 6897x * (10 + x) + 2392x2 * (10 + x) + 398x3 * (10 + x) + 32x4 * (10 + x) + x5(10 + x))) 0 = ((75600 + 7560x + (10 * 6897x + x * 6897x) + 2392x2 * (10 + x) + 398x3 * (10 + x) + 32x4 * (10 + x) + x5(10 + x))) 0 = ((75600 + 7560x + (68970x + 6897x2) + 2392x2 * (10 + x) + 398x3 * (10 + x) + 32x4 * (10 + x) + x5(10 + x))) 0 = ((75600 + 7560x + 68970x + 6897x2 + (10 * 2392x2 + x * 2392x2) + 398x3 * (10 + x) + 32x4 * (10 + x) + x5(10 + x))) 0 = ((75600 + 7560x + 68970x + 6897x2 + (23920x2 + 2392x3) + 398x3 * (10 + x) + 32x4 * (10 + x) + x5(10 + x))) 0 = ((75600 + 7560x + 68970x + 6897x2 + 23920x2 + 2392x3 + (10 * 398x3 + x * 398x3) + 32x4 * (10 + x) + x5(10 + x))) 0 = ((75600 + 7560x + 68970x + 6897x2 + 23920x2 + 2392x3 + (3980x3 + 398x4) + 32x4 * (10 + x) + x5(10 + x))) 0 = ((75600 + 7560x + 68970x + 6897x2 + 23920x2 + 2392x3 + 3980x3 + 398x4 + (10 * 32x4 + x * 32x4) + x5(10 + x))) 0 = ((75600 + 7560x + 68970x + 6897x2 + 23920x2 + 2392x3 + 3980x3 + 398x4 + (320x4 + 32x5) + x5(10 + x))) 0 = ((75600 + 7560x + 68970x + 6897x2 + 23920x2 + 2392x3 + 3980x3 + 398x4 + 320x4 + 32x5 + (10 * x5 + x * x5))) 0 = ((75600 + 7560x + 68970x + 6897x2 + 23920x2 + 2392x3 + 3980x3 + 398x4 + 320x4 + 32x5 + (10x5 + x6))) Combine like terms: 7560x + 68970x = 76530x 0 = ((75600 + 76530x + 6897x2 + 23920x2 + 2392x3 + 3980x3 + 398x4 + 320x4 + 32x5 + 10x5 + x6)) Combine like terms: 6897x2 + 23920x2 = 30817x2 0 = ((75600 + 76530x + 30817x2 + 2392x3 + 3980x3 + 398x4 + 320x4 + 32x5 + 10x5 + x6)) Combine like terms: 2392x3 + 3980x3 = 6372x3 0 = ((75600 + 76530x + 30817x2 + 6372x3 + 398x4 + 320x4 + 32x5 + 10x5 + x6)) Combine like terms: 398x4 + 320x4 = 718x4 0 = ((75600 + 76530x + 30817x2 + 6372x3 + 718x4 + 32x5 + 10x5 + x6)) Combine like terms: 32x5 + 10x5 = 42x5 0 = ((75600 + 76530x + 30817x2 + 6372x3 + 718x4 + 42x5 + x6)) 0 = (75600 + 76530x + 30817x2 + 6372x3 + 718x4 + 42x5 + x6) Remove parenthesis around (75600 + 76530x + 30817x2 + 6372x3 + 718x4 + 42x5 + x6) 0 = 75600 + 76530x + 30817x2 + 6372x3 + 718x4 + 42x5 + x6 Solving 0 = 75600 + 76530x + 30817x2 + 6372x3 + 718x4 + 42x5 + x6 Solving for variable 'x'. Combine like terms: 0 + -75600 = -75600 -75600 + -76530x + -30817x2 + -6372x3 + -718x4 + -42x5 + -1x6 = 75600 + 76530x + 30817x2 + 6372x3 + 718x4 + 42x5 + x6 + -75600 + -76530x + -30817x2 + -6372x3 + -718x4 + -42x5 + -1x6 Reorder the terms: -75600 + -76530x + -30817x2 + -6372x3 + -718x4 + -42x5 + -1x6 = 75600 + -75600 + 76530x + -76530x + 30817x2 + -30817x2 + 6372x3 + -6372x3 + 718x4 + -718x4 + 42x5 + -42x5 + x6 + -1x6 Combine like terms: 75600 + -75600 = 0 -75600 + -76530x + -30817x2 + -6372x3 + -718x4 + -42x5 + -1x6 = 0 + 76530x + -76530x + 30817x2 + -30817x2 + 6372x3 + -6372x3 + 718x4 + -718x4 + 42x5 + -42x5 + x6 + -1x6 -75600 + -76530x + -30817x2 + -6372x3 + -718x4 + -42x5 + -1x6 = 76530x + -76530x + 30817x2 + -30817x2 + 6372x3 + -6372x3 + 718x4 + -718x4 + 42x5 + -42x5 + x6 + -1x6 Combine like terms: 76530x + -76530x = 0 -75600 + -76530x + -30817x2 + -6372x3 + -718x4 + -42x5 + -1x6 = 0 + 30817x2 + -30817x2 + 6372x3 + -6372x3 + 718x4 + -718x4 + 42x5 + -42x5 + x6 + -1x6 -75600 + -76530x + -30817x2 + -6372x3 + -718x4 + -42x5 + -1x6 = 30817x2 + -30817x2 + 6372x3 + -6372x3 + 718x4 + -718x4 + 42x5 + -42x5 + x6 + -1x6 Combine like terms: 30817x2 + -30817x2 = 0 -75600 + -76530x + -30817x2 + -6372x3 + -718x4 + -42x5 + -1x6 = 0 + 6372x3 + -6372x3 + 718x4 + -718x4 + 42x5 + -42x5 + x6 + -1x6 -75600 + -76530x + -30817x2 + -6372x3 + -718x4 + -42x5 + -1x6 = 6372x3 + -6372x3 + 718x4 + -718x4 + 42x5 + -42x5 + x6 + -1x6 Combine like terms: 6372x3 + -6372x3 = 0 -75600 + -76530x + -30817x2 + -6372x3 + -718x4 + -42x5 + -1x6 = 0 + 718x4 + -718x4 + 42x5 + -42x5 + x6 + -1x6 -75600 + -76530x + -30817x2 + -6372x3 + -718x4 + -42x5 + -1x6 = 718x4 + -718x4 + 42x5 + -42x5 + x6 + -1x6 Combine like terms: 718x4 + -718x4 = 0 -75600 + -76530x + -30817x2 + -6372x3 + -718x4 + -42x5 + -1x6 = 0 + 42x5 + -42x5 + x6 + -1x6 -75600 + -76530x + -30817x2 + -6372x3 + -718x4 + -42x5 + -1x6 = 42x5 + -42x5 + x6 + -1x6 Combine like terms: 42x5 + -42x5 = 0 -75600 + -76530x + -30817x2 + -6372x3 + -718x4 + -42x5 + -1x6 = 0 + x6 + -1x6 -75600 + -76530x + -30817x2 + -6372x3 + -718x4 + -42x5 + -1x6 = x6 + -1x6 Combine like terms: x6 + -1x6 = 0 -75600 + -76530x + -30817x2 + -6372x3 + -718x4 + -42x5 + -1x6 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(75600 + 76530x + 30817x2 + 6372x3 + 718x4 + 42x5 + x6) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(75600 + 76530x + 30817x2 + 6372x3 + 718x4 + 42x5 + x6)' equal to zero and attempt to solve: Simplifying 75600 + 76530x + 30817x2 + 6372x3 + 718x4 + 42x5 + x6 = 0 Solving 75600 + 76530x + 30817x2 + 6372x3 + 718x4 + 42x5 + x6 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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