(X+a)(x+2a)(x+3a)(x+4a)=b^4

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Solution for (X+a)(x+2a)(x+3a)(x+4a)=b^4 equation: 


Simplifying
(X + a)(x + 2a)(x + 3a)(x + 4a) = b4

Reorder the terms:
(X + a)(2a + x)(x + 3a)(x + 4a) = b4

Reorder the terms:
(X + a)(2a + x)(3a + x)(x + 4a) = b4

Reorder the terms:
(X + a)(2a + x)(3a + x)(4a + x) = b4

Multiply (X + a) * (2a + x)
(X(2a + x) + a(2a + x))(3a + x)(4a + x) = b4
((2a * X + x * X) + a(2a + x))(3a + x)(4a + x) = b4
((2aX + xX) + a(2a + x))(3a + x)(4a + x) = b4
(2aX + xX + (2a * a + x * a))(3a + x)(4a + x) = b4

Reorder the terms:
(2aX + xX + (ax + 2a2))(3a + x)(4a + x) = b4
(2aX + xX + (ax + 2a2))(3a + x)(4a + x) = b4

Reorder the terms:
(2aX + ax + 2a2 + xX)(3a + x)(4a + x) = b4
(2aX + ax + 2a2 + xX)(3a + x)(4a + x) = b4

Multiply (2aX + ax + 2a2 + xX) * (3a + x)
(2aX * (3a + x) + ax(3a + x) + 2a2 * (3a + x) + xX(3a + x))(4a + x) = b4
((3a * 2aX + x * 2aX) + ax(3a + x) + 2a2 * (3a + x) + xX(3a + x))(4a + x) = b4

Reorder the terms:
((2axX + 6a2X) + ax(3a + x) + 2a2 * (3a + x) + xX(3a + x))(4a + x) = b4
((2axX + 6a2X) + ax(3a + x) + 2a2 * (3a + x) + xX(3a + x))(4a + x) = b4
(2axX + 6a2X + (3a * ax + x * ax) + 2a2 * (3a + x) + xX(3a + x))(4a + x) = b4

Reorder the terms:
(2axX + 6a2X + (ax2 + 3a2x) + 2a2 * (3a + x) + xX(3a + x))(4a + x) = b4
(2axX + 6a2X + (ax2 + 3a2x) + 2a2 * (3a + x) + xX(3a + x))(4a + x) = b4
(2axX + 6a2X + ax2 + 3a2x + (3a * 2a2 + x * 2a2) + xX(3a + x))(4a + x) = b4

Reorder the terms:
(2axX + 6a2X + ax2 + 3a2x + (2a2x + 6a3) + xX(3a + x))(4a + x) = b4
(2axX + 6a2X + ax2 + 3a2x + (2a2x + 6a3) + xX(3a + x))(4a + x) = b4
(2axX + 6a2X + ax2 + 3a2x + 2a2x + 6a3 + (3a * xX + x * xX))(4a + x) = b4
(2axX + 6a2X + ax2 + 3a2x + 2a2x + 6a3 + (3axX + x2X))(4a + x) = b4

Reorder the terms:
(2axX + 3axX + ax2 + 6a2X + 3a2x + 2a2x + 6a3 + x2X)(4a + x) = b4

Combine like terms: 2axX + 3axX = 5axX
(5axX + ax2 + 6a2X + 3a2x + 2a2x + 6a3 + x2X)(4a + x) = b4

Combine like terms: 3a2x + 2a2x = 5a2x
(5axX + ax2 + 6a2X + 5a2x + 6a3 + x2X)(4a + x) = b4

Multiply (5axX + ax2 + 6a2X + 5a2x + 6a3 + x2X) * (4a + x)
(5axX * (4a + x) + ax2(4a + x) + 6a2X * (4a + x) + 5a2x * (4a + x) + 6a3 * (4a + x) + x2X(4a + x)) = b4
((4a * 5axX + x * 5axX) + ax2(4a + x) + 6a2X * (4a + x) + 5a2x * (4a + x) + 6a3 * (4a + x) + x2X(4a + x)) = b4

Reorder the terms:
((5ax2X + 20a2xX) + ax2(4a + x) + 6a2X * (4a + x) + 5a2x * (4a + x) + 6a3 * (4a + x) + x2X(4a + x)) = b4
((5ax2X + 20a2xX) + ax2(4a + x) + 6a2X * (4a + x) + 5a2x * (4a + x) + 6a3 * (4a + x) + x2X(4a + x)) = b4
(5ax2X + 20a2xX + (4a * ax2 + x * ax2) + 6a2X * (4a + x) + 5a2x * (4a + x) + 6a3 * (4a + x) + x2X(4a + x)) = b4

Reorder the terms:
(5ax2X + 20a2xX + (ax3 + 4a2x2) + 6a2X * (4a + x) + 5a2x * (4a + x) + 6a3 * (4a + x) + x2X(4a + x)) = b4
(5ax2X + 20a2xX + (ax3 + 4a2x2) + 6a2X * (4a + x) + 5a2x * (4a + x) + 6a3 * (4a + x) + x2X(4a + x)) = b4
(5ax2X + 20a2xX + ax3 + 4a2x2 + (4a * 6a2X + x * 6a2X) + 5a2x * (4a + x) + 6a3 * (4a + x) + x2X(4a + x)) = b4

Reorder the terms:
(5ax2X + 20a2xX + ax3 + 4a2x2 + (6a2xX + 24a3X) + 5a2x * (4a + x) + 6a3 * (4a + x) + x2X(4a + x)) = b4
(5ax2X + 20a2xX + ax3 + 4a2x2 + (6a2xX + 24a3X) + 5a2x * (4a + x) + 6a3 * (4a + x) + x2X(4a + x)) = b4
(5ax2X + 20a2xX + ax3 + 4a2x2 + 6a2xX + 24a3X + (4a * 5a2x + x * 5a2x) + 6a3 * (4a + x) + x2X(4a + x)) = b4

Reorder the terms:
(5ax2X + 20a2xX + ax3 + 4a2x2 + 6a2xX + 24a3X + (5a2x2 + 20a3x) + 6a3 * (4a + x) + x2X(4a + x)) = b4
(5ax2X + 20a2xX + ax3 + 4a2x2 + 6a2xX + 24a3X + (5a2x2 + 20a3x) + 6a3 * (4a + x) + x2X(4a + x)) = b4
(5ax2X + 20a2xX + ax3 + 4a2x2 + 6a2xX + 24a3X + 5a2x2 + 20a3x + (4a * 6a3 + x * 6a3) + x2X(4a + x)) = b4

Reorder the terms:
(5ax2X + 20a2xX + ax3 + 4a2x2 + 6a2xX + 24a3X + 5a2x2 + 20a3x + (6a3x + 24a4) + x2X(4a + x)) = b4
(5ax2X + 20a2xX + ax3 + 4a2x2 + 6a2xX + 24a3X + 5a2x2 + 20a3x + (6a3x + 24a4) + x2X(4a + x)) = b4
(5ax2X + 20a2xX + ax3 + 4a2x2 + 6a2xX + 24a3X + 5a2x2 + 20a3x + 6a3x + 24a4 + (4a * x2X + x * x2X)) = b4
(5ax2X + 20a2xX + ax3 + 4a2x2 + 6a2xX + 24a3X + 5a2x2 + 20a3x + 6a3x + 24a4 + (4ax2X + x3X)) = b4

Reorder the terms:
(5ax2X + 4ax2X + ax3 + 20a2xX + 6a2xX + 4a2x2 + 5a2x2 + 24a3X + 20a3x + 6a3x + 24a4 + x3X) = b4

Combine like terms: 5ax2X + 4ax2X = 9ax2X
(9ax2X + ax3 + 20a2xX + 6a2xX + 4a2x2 + 5a2x2 + 24a3X + 20a3x + 6a3x + 24a4 + x3X) = b4

Combine like terms: 20a2xX + 6a2xX = 26a2xX
(9ax2X + ax3 + 26a2xX + 4a2x2 + 5a2x2 + 24a3X + 20a3x + 6a3x + 24a4 + x3X) = b4

Combine like terms: 4a2x2 + 5a2x2 = 9a2x2
(9ax2X + ax3 + 26a2xX + 9a2x2 + 24a3X + 20a3x + 6a3x + 24a4 + x3X) = b4

Combine like terms: 20a3x + 6a3x = 26a3x
(9ax2X + ax3 + 26a2xX + 9a2x2 + 24a3X + 26a3x + 24a4 + x3X) = b4

Solving
9ax2X + ax3 + 26a2xX + 9a2x2 + 24a3X + 26a3x + 24a4 + x3X = b4

Solving for variable 'a'.

Reorder the terms:
9ax2X + ax3 + 26a2xX + 9a2x2 + 24a3X + 26a3x + 24a4 + -1b4 + x3X = b4 + -1b4

Combine like terms: b4 + -1b4 = 0
9ax2X + ax3 + 26a2xX + 9a2x2 + 24a3X + 26a3x + 24a4 + -1b4 + x3X = 0

The solution to this equation could not be determined.

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