(x+1)(x+3)(x+5)(x+7)=105

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Solution for (x+1)(x+3)(x+5)(x+7)=105 equation: 


Simplifying
(x + 1)(x + 3)(x + 5)(x + 7) = 105

Reorder the terms:
(1 + x)(x + 3)(x + 5)(x + 7) = 105

Reorder the terms:
(1 + x)(3 + x)(x + 5)(x + 7) = 105

Reorder the terms:
(1 + x)(3 + x)(5 + x)(x + 7) = 105

Reorder the terms:
(1 + x)(3 + x)(5 + x)(7 + x) = 105

Multiply (1 + x) * (3 + x)
(1(3 + x) + x(3 + x))(5 + x)(7 + x) = 105
((3 * 1 + x * 1) + x(3 + x))(5 + x)(7 + x) = 105
((3 + 1x) + x(3 + x))(5 + x)(7 + x) = 105
(3 + 1x + (3 * x + x * x))(5 + x)(7 + x) = 105
(3 + 1x + (3x + x2))(5 + x)(7 + x) = 105

Combine like terms: 1x + 3x = 4x
(3 + 4x + x2)(5 + x)(7 + x) = 105

Multiply (3 + 4x + x2) * (5 + x)
(3(5 + x) + 4x * (5 + x) + x2(5 + x))(7 + x) = 105
((5 * 3 + x * 3) + 4x * (5 + x) + x2(5 + x))(7 + x) = 105
((15 + 3x) + 4x * (5 + x) + x2(5 + x))(7 + x) = 105
(15 + 3x + (5 * 4x + x * 4x) + x2(5 + x))(7 + x) = 105
(15 + 3x + (20x + 4x2) + x2(5 + x))(7 + x) = 105
(15 + 3x + 20x + 4x2 + (5 * x2 + x * x2))(7 + x) = 105
(15 + 3x + 20x + 4x2 + (5x2 + x3))(7 + x) = 105

Combine like terms: 3x + 20x = 23x
(15 + 23x + 4x2 + 5x2 + x3)(7 + x) = 105

Combine like terms: 4x2 + 5x2 = 9x2
(15 + 23x + 9x2 + x3)(7 + x) = 105

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

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

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

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

Add '-105' to each side of the equation.
105 + 176x + 86x2 + 16x3 + -105 + x4 = 105 + -105

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

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

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

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

Solving for variable 'x'.

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


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0

Subproblem 2
Set the factor '(176 + 86x + 16x2 + x3)' equal to zero and attempt to solve:

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

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

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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