=(x+1)(x+3)(x+5)(x+7)

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Solution for =(x+1)(x+3)(x+5)(x+7) equation: 


Simplifying
0 = (x + 1)(x + 3)(x + 5)(x + 7)

Reorder the terms:
0 = (1 + x)(x + 3)(x + 5)(x + 7)

Reorder the terms:
0 = (1 + x)(3 + x)(x + 5)(x + 7)

Reorder the terms:
0 = (1 + x)(3 + x)(5 + x)(x + 7)

Reorder the terms:
0 = (1 + x)(3 + x)(5 + x)(7 + x)

Multiply (1 + x) * (3 + x)
0 = (1(3 + x) + x(3 + x))(5 + x)(7 + x)
0 = ((3 * 1 + x * 1) + x(3 + x))(5 + x)(7 + x)
0 = ((3 + 1x) + x(3 + x))(5 + x)(7 + x)
0 = (3 + 1x + (3 * x + x * x))(5 + x)(7 + x)
0 = (3 + 1x + (3x + x2))(5 + x)(7 + x)

Combine like terms: 1x + 3x = 4x
0 = (3 + 4x + x2)(5 + x)(7 + x)

Multiply (3 + 4x + x2) * (5 + x)
0 = (3(5 + x) + 4x * (5 + x) + x2(5 + x))(7 + x)
0 = ((5 * 3 + x * 3) + 4x * (5 + x) + x2(5 + x))(7 + x)
0 = ((15 + 3x) + 4x * (5 + x) + x2(5 + x))(7 + x)
0 = (15 + 3x + (5 * 4x + x * 4x) + x2(5 + x))(7 + x)
0 = (15 + 3x + (20x + 4x2) + x2(5 + x))(7 + x)
0 = (15 + 3x + 20x + 4x2 + (5 * x2 + x * x2))(7 + x)
0 = (15 + 3x + 20x + 4x2 + (5x2 + x3))(7 + x)

Combine like terms: 3x + 20x = 23x
0 = (15 + 23x + 4x2 + 5x2 + x3)(7 + x)

Combine like terms: 4x2 + 5x2 = 9x2
0 = (15 + 23x + 9x2 + x3)(7 + x)

Multiply (15 + 23x + 9x2 + x3) * (7 + x)
0 = (15(7 + x) + 23x * (7 + x) + 9x2 * (7 + x) + x3(7 + x))
0 = ((7 * 15 + x * 15) + 23x * (7 + x) + 9x2 * (7 + x) + x3(7 + x))
0 = ((105 + 15x) + 23x * (7 + x) + 9x2 * (7 + x) + x3(7 + x))
0 = (105 + 15x + (7 * 23x + x * 23x) + 9x2 * (7 + x) + x3(7 + x))
0 = (105 + 15x + (161x + 23x2) + 9x2 * (7 + x) + x3(7 + x))
0 = (105 + 15x + 161x + 23x2 + (7 * 9x2 + x * 9x2) + x3(7 + x))
0 = (105 + 15x + 161x + 23x2 + (63x2 + 9x3) + x3(7 + x))
0 = (105 + 15x + 161x + 23x2 + 63x2 + 9x3 + (7 * x3 + x * x3))
0 = (105 + 15x + 161x + 23x2 + 63x2 + 9x3 + (7x3 + x4))

Combine like terms: 15x + 161x = 176x
0 = (105 + 176x + 23x2 + 63x2 + 9x3 + 7x3 + x4)

Combine like terms: 23x2 + 63x2 = 86x2
0 = (105 + 176x + 86x2 + 9x3 + 7x3 + x4)

Combine like terms: 9x3 + 7x3 = 16x3
0 = (105 + 176x + 86x2 + 16x3 + x4)

Solving
0 = 105 + 176x + 86x2 + 16x3 + x4

Solving for variable 'x'.

Combine like terms: 0 + -105 = -105
-105 + -176x + -86x2 + -16x3 + -1x4 = 105 + 176x + 86x2 + 16x3 + x4 + -105 + -176x + -86x2 + -16x3 + -1x4

Reorder the terms:
-105 + -176x + -86x2 + -16x3 + -1x4 = 105 + -105 + 176x + -176x + 86x2 + -86x2 + 16x3 + -16x3 + x4 + -1x4

Combine like terms: 105 + -105 = 0
-105 + -176x + -86x2 + -16x3 + -1x4 = 0 + 176x + -176x + 86x2 + -86x2 + 16x3 + -16x3 + x4 + -1x4
-105 + -176x + -86x2 + -16x3 + -1x4 = 176x + -176x + 86x2 + -86x2 + 16x3 + -16x3 + x4 + -1x4

Combine like terms: 176x + -176x = 0
-105 + -176x + -86x2 + -16x3 + -1x4 = 0 + 86x2 + -86x2 + 16x3 + -16x3 + x4 + -1x4
-105 + -176x + -86x2 + -16x3 + -1x4 = 86x2 + -86x2 + 16x3 + -16x3 + x4 + -1x4

Combine like terms: 86x2 + -86x2 = 0
-105 + -176x + -86x2 + -16x3 + -1x4 = 0 + 16x3 + -16x3 + x4 + -1x4
-105 + -176x + -86x2 + -16x3 + -1x4 = 16x3 + -16x3 + x4 + -1x4

Combine like terms: 16x3 + -16x3 = 0
-105 + -176x + -86x2 + -16x3 + -1x4 = 0 + x4 + -1x4
-105 + -176x + -86x2 + -16x3 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
-105 + -176x + -86x2 + -16x3 + -1x4 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(105 + 176x + 86x2 + 16x3 + x4) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(105 + 176x + 86x2 + 16x3 + x4)' equal to zero and attempt to solve:

Simplifying
105 + 176x + 86x2 + 16x3 + x4 = 0

Solving
105 + 176x + 86x2 + 16x3 + x4 = 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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