(x+2n)(x-6a)(x+3a)(x-3a)=180a^4

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Solution for (x+2n)(x-6a)(x+3a)(x-3a)=180a^4 equation: 


Simplifying
(x + 2n)(x + -6a)(x + 3a)(x + -3a) = 180a4

Reorder the terms:
(2n + x)(x + -6a)(x + 3a)(x + -3a) = 180a4

Reorder the terms:
(2n + x)(-6a + x)(x + 3a)(x + -3a) = 180a4

Reorder the terms:
(2n + x)(-6a + x)(3a + x)(x + -3a) = 180a4

Reorder the terms:
(2n + x)(-6a + x)(3a + x)(-3a + x) = 180a4

Multiply (2n + x) * (-6a + x)
(2n * (-6a + x) + x(-6a + x))(3a + x)(-3a + x) = 180a4
((-6a * 2n + x * 2n) + x(-6a + x))(3a + x)(-3a + x) = 180a4
((-12an + 2nx) + x(-6a + x))(3a + x)(-3a + x) = 180a4
(-12an + 2nx + (-6a * x + x * x))(3a + x)(-3a + x) = 180a4
(-12an + 2nx + (-6ax + x2))(3a + x)(-3a + x) = 180a4

Reorder the terms:
(-12an + -6ax + 2nx + x2)(3a + x)(-3a + x) = 180a4
(-12an + -6ax + 2nx + x2)(3a + x)(-3a + x) = 180a4

Multiply (-12an + -6ax + 2nx + x2) * (3a + x)
(-12an * (3a + x) + -6ax * (3a + x) + 2nx * (3a + x) + x2(3a + x))(-3a + x) = 180a4
((3a * -12an + x * -12an) + -6ax * (3a + x) + 2nx * (3a + x) + x2(3a + x))(-3a + x) = 180a4

Reorder the terms:
((-12anx + -36a2n) + -6ax * (3a + x) + 2nx * (3a + x) + x2(3a + x))(-3a + x) = 180a4
((-12anx + -36a2n) + -6ax * (3a + x) + 2nx * (3a + x) + x2(3a + x))(-3a + x) = 180a4
(-12anx + -36a2n + (3a * -6ax + x * -6ax) + 2nx * (3a + x) + x2(3a + x))(-3a + x) = 180a4

Reorder the terms:
(-12anx + -36a2n + (-6ax2 + -18a2x) + 2nx * (3a + x) + x2(3a + x))(-3a + x) = 180a4
(-12anx + -36a2n + (-6ax2 + -18a2x) + 2nx * (3a + x) + x2(3a + x))(-3a + x) = 180a4
(-12anx + -36a2n + -6ax2 + -18a2x + (3a * 2nx + x * 2nx) + x2(3a + x))(-3a + x) = 180a4
(-12anx + -36a2n + -6ax2 + -18a2x + (6anx + 2nx2) + x2(3a + x))(-3a + x) = 180a4
(-12anx + -36a2n + -6ax2 + -18a2x + 6anx + 2nx2 + (3a * x2 + x * x2))(-3a + x) = 180a4
(-12anx + -36a2n + -6ax2 + -18a2x + 6anx + 2nx2 + (3ax2 + x3))(-3a + x) = 180a4

Reorder the terms:
(-12anx + 6anx + -6ax2 + 3ax2 + -36a2n + -18a2x + 2nx2 + x3)(-3a + x) = 180a4

Combine like terms: -12anx + 6anx = -6anx
(-6anx + -6ax2 + 3ax2 + -36a2n + -18a2x + 2nx2 + x3)(-3a + x) = 180a4

Combine like terms: -6ax2 + 3ax2 = -3ax2
(-6anx + -3ax2 + -36a2n + -18a2x + 2nx2 + x3)(-3a + x) = 180a4

Multiply (-6anx + -3ax2 + -36a2n + -18a2x + 2nx2 + x3) * (-3a + x)
(-6anx * (-3a + x) + -3ax2 * (-3a + x) + -36a2n * (-3a + x) + -18a2x * (-3a + x) + 2nx2 * (-3a + x) + x3(-3a + x)) = 180a4
((-3a * -6anx + x * -6anx) + -3ax2 * (-3a + x) + -36a2n * (-3a + x) + -18a2x * (-3a + x) + 2nx2 * (-3a + x) + x3(-3a + x)) = 180a4

Reorder the terms:
((-6anx2 + 18a2nx) + -3ax2 * (-3a + x) + -36a2n * (-3a + x) + -18a2x * (-3a + x) + 2nx2 * (-3a + x) + x3(-3a + x)) = 180a4
((-6anx2 + 18a2nx) + -3ax2 * (-3a + x) + -36a2n * (-3a + x) + -18a2x * (-3a + x) + 2nx2 * (-3a + x) + x3(-3a + x)) = 180a4
(-6anx2 + 18a2nx + (-3a * -3ax2 + x * -3ax2) + -36a2n * (-3a + x) + -18a2x * (-3a + x) + 2nx2 * (-3a + x) + x3(-3a + x)) = 180a4

Reorder the terms:
(-6anx2 + 18a2nx + (-3ax3 + 9a2x2) + -36a2n * (-3a + x) + -18a2x * (-3a + x) + 2nx2 * (-3a + x) + x3(-3a + x)) = 180a4
(-6anx2 + 18a2nx + (-3ax3 + 9a2x2) + -36a2n * (-3a + x) + -18a2x * (-3a + x) + 2nx2 * (-3a + x) + x3(-3a + x)) = 180a4
(-6anx2 + 18a2nx + -3ax3 + 9a2x2 + (-3a * -36a2n + x * -36a2n) + -18a2x * (-3a + x) + 2nx2 * (-3a + x) + x3(-3a + x)) = 180a4

Reorder the terms:
(-6anx2 + 18a2nx + -3ax3 + 9a2x2 + (-36a2nx + 108a3n) + -18a2x * (-3a + x) + 2nx2 * (-3a + x) + x3(-3a + x)) = 180a4
(-6anx2 + 18a2nx + -3ax3 + 9a2x2 + (-36a2nx + 108a3n) + -18a2x * (-3a + x) + 2nx2 * (-3a + x) + x3(-3a + x)) = 180a4
(-6anx2 + 18a2nx + -3ax3 + 9a2x2 + -36a2nx + 108a3n + (-3a * -18a2x + x * -18a2x) + 2nx2 * (-3a + x) + x3(-3a + x)) = 180a4

Reorder the terms:
(-6anx2 + 18a2nx + -3ax3 + 9a2x2 + -36a2nx + 108a3n + (-18a2x2 + 54a3x) + 2nx2 * (-3a + x) + x3(-3a + x)) = 180a4
(-6anx2 + 18a2nx + -3ax3 + 9a2x2 + -36a2nx + 108a3n + (-18a2x2 + 54a3x) + 2nx2 * (-3a + x) + x3(-3a + x)) = 180a4
(-6anx2 + 18a2nx + -3ax3 + 9a2x2 + -36a2nx + 108a3n + -18a2x2 + 54a3x + (-3a * 2nx2 + x * 2nx2) + x3(-3a + x)) = 180a4
(-6anx2 + 18a2nx + -3ax3 + 9a2x2 + -36a2nx + 108a3n + -18a2x2 + 54a3x + (-6anx2 + 2nx3) + x3(-3a + x)) = 180a4
(-6anx2 + 18a2nx + -3ax3 + 9a2x2 + -36a2nx + 108a3n + -18a2x2 + 54a3x + -6anx2 + 2nx3 + (-3a * x3 + x * x3)) = 180a4
(-6anx2 + 18a2nx + -3ax3 + 9a2x2 + -36a2nx + 108a3n + -18a2x2 + 54a3x + -6anx2 + 2nx3 + (-3ax3 + x4)) = 180a4

Reorder the terms:
(-6anx2 + -6anx2 + -3ax3 + -3ax3 + 18a2nx + -36a2nx + 9a2x2 + -18a2x2 + 108a3n + 54a3x + 2nx3 + x4) = 180a4

Combine like terms: -6anx2 + -6anx2 = -12anx2
(-12anx2 + -3ax3 + -3ax3 + 18a2nx + -36a2nx + 9a2x2 + -18a2x2 + 108a3n + 54a3x + 2nx3 + x4) = 180a4

Combine like terms: -3ax3 + -3ax3 = -6ax3
(-12anx2 + -6ax3 + 18a2nx + -36a2nx + 9a2x2 + -18a2x2 + 108a3n + 54a3x + 2nx3 + x4) = 180a4

Combine like terms: 18a2nx + -36a2nx = -18a2nx
(-12anx2 + -6ax3 + -18a2nx + 9a2x2 + -18a2x2 + 108a3n + 54a3x + 2nx3 + x4) = 180a4

Combine like terms: 9a2x2 + -18a2x2 = -9a2x2
(-12anx2 + -6ax3 + -18a2nx + -9a2x2 + 108a3n + 54a3x + 2nx3 + x4) = 180a4

Solving
-12anx2 + -6ax3 + -18a2nx + -9a2x2 + 108a3n + 54a3x + 2nx3 + x4 = 180a4

Solving for variable 'a'.

Reorder the terms:
-12anx2 + -6ax3 + -18a2nx + -9a2x2 + 108a3n + 54a3x + -180a4 + 2nx3 + x4 = 180a4 + -180a4

Combine like terms: 180a4 + -180a4 = 0
-12anx2 + -6ax3 + -18a2nx + -9a2x2 + 108a3n + 54a3x + -180a4 + 2nx3 + x4 = 0

The solution to this equation could not be determined.

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