15x^2(3x-1)(3x-1)(3x-1)(3x-1)+60x^3(3x-1)(3x-1)(3x-1)=0

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Solution for 15x^2(3x-1)(3x-1)(3x-1)(3x-1)+60x^3(3x-1)(3x-1)(3x-1)=0 equation: 


Simplifying
15x2(3x + -1)(3x + -1)(3x + -1)(3x + -1) + 60x3(3x + -1)(3x + -1)(3x + -1) = 0

Reorder the terms:
15x2(-1 + 3x)(3x + -1)(3x + -1)(3x + -1) + 60x3(3x + -1)(3x + -1)(3x + -1) = 0

Reorder the terms:
15x2(-1 + 3x)(-1 + 3x)(3x + -1)(3x + -1) + 60x3(3x + -1)(3x + -1)(3x + -1) = 0

Reorder the terms:
15x2(-1 + 3x)(-1 + 3x)(-1 + 3x)(3x + -1) + 60x3(3x + -1)(3x + -1)(3x + -1) = 0

Reorder the terms:
15x2(-1 + 3x)(-1 + 3x)(-1 + 3x)(-1 + 3x) + 60x3(3x + -1)(3x + -1)(3x + -1) = 0

Multiply (-1 + 3x) * (-1 + 3x)
15x2(-1(-1 + 3x) + 3x * (-1 + 3x))(-1 + 3x)(-1 + 3x) + 60x3(3x + -1)(3x + -1)(3x + -1) = 0
15x2((-1 * -1 + 3x * -1) + 3x * (-1 + 3x))(-1 + 3x)(-1 + 3x) + 60x3(3x + -1)(3x + -1)(3x + -1) = 0
15x2((1 + -3x) + 3x * (-1 + 3x))(-1 + 3x)(-1 + 3x) + 60x3(3x + -1)(3x + -1)(3x + -1) = 0
15x2(1 + -3x + (-1 * 3x + 3x * 3x))(-1 + 3x)(-1 + 3x) + 60x3(3x + -1)(3x + -1)(3x + -1) = 0
15x2(1 + -3x + (-3x + 9x2))(-1 + 3x)(-1 + 3x) + 60x3(3x + -1)(3x + -1)(3x + -1) = 0

Combine like terms: -3x + -3x = -6x
15x2(1 + -6x + 9x2)(-1 + 3x)(-1 + 3x) + 60x3(3x + -1)(3x + -1)(3x + -1) = 0

Multiply (1 + -6x + 9x2) * (-1 + 3x)
15x2(1(-1 + 3x) + -6x * (-1 + 3x) + 9x2 * (-1 + 3x))(-1 + 3x) + 60x3(3x + -1)(3x + -1)(3x + -1) = 0
15x2((-1 * 1 + 3x * 1) + -6x * (-1 + 3x) + 9x2 * (-1 + 3x))(-1 + 3x) + 60x3(3x + -1)(3x + -1)(3x + -1) = 0
15x2((-1 + 3x) + -6x * (-1 + 3x) + 9x2 * (-1 + 3x))(-1 + 3x) + 60x3(3x + -1)(3x + -1)(3x + -1) = 0
15x2(-1 + 3x + (-1 * -6x + 3x * -6x) + 9x2 * (-1 + 3x))(-1 + 3x) + 60x3(3x + -1)(3x + -1)(3x + -1) = 0
15x2(-1 + 3x + (6x + -18x2) + 9x2 * (-1 + 3x))(-1 + 3x) + 60x3(3x + -1)(3x + -1)(3x + -1) = 0
15x2(-1 + 3x + 6x + -18x2 + (-1 * 9x2 + 3x * 9x2))(-1 + 3x) + 60x3(3x + -1)(3x + -1)(3x + -1) = 0
15x2(-1 + 3x + 6x + -18x2 + (-9x2 + 27x3))(-1 + 3x) + 60x3(3x + -1)(3x + -1)(3x + -1) = 0

Combine like terms: 3x + 6x = 9x
15x2(-1 + 9x + -18x2 + -9x2 + 27x3)(-1 + 3x) + 60x3(3x + -1)(3x + -1)(3x + -1) = 0

Combine like terms: -18x2 + -9x2 = -27x2
15x2(-1 + 9x + -27x2 + 27x3)(-1 + 3x) + 60x3(3x + -1)(3x + -1)(3x + -1) = 0

Multiply (-1 + 9x + -27x2 + 27x3) * (-1 + 3x)
15x2(-1(-1 + 3x) + 9x * (-1 + 3x) + -27x2 * (-1 + 3x) + 27x3 * (-1 + 3x)) + 60x3(3x + -1)(3x + -1)(3x + -1) = 0
15x2((-1 * -1 + 3x * -1) + 9x * (-1 + 3x) + -27x2 * (-1 + 3x) + 27x3 * (-1 + 3x)) + 60x3(3x + -1)(3x + -1)(3x + -1) = 0
15x2((1 + -3x) + 9x * (-1 + 3x) + -27x2 * (-1 + 3x) + 27x3 * (-1 + 3x)) + 60x3(3x + -1)(3x + -1)(3x + -1) = 0
15x2(1 + -3x + (-1 * 9x + 3x * 9x) + -27x2 * (-1 + 3x) + 27x3 * (-1 + 3x)) + 60x3(3x + -1)(3x + -1)(3x + -1) = 0
15x2(1 + -3x + (-9x + 27x2) + -27x2 * (-1 + 3x) + 27x3 * (-1 + 3x)) + 60x3(3x + -1)(3x + -1)(3x + -1) = 0
15x2(1 + -3x + -9x + 27x2 + (-1 * -27x2 + 3x * -27x2) + 27x3 * (-1 + 3x)) + 60x3(3x + -1)(3x + -1)(3x + -1) = 0
15x2(1 + -3x + -9x + 27x2 + (27x2 + -81x3) + 27x3 * (-1 + 3x)) + 60x3(3x + -1)(3x + -1)(3x + -1) = 0
15x2(1 + -3x + -9x + 27x2 + 27x2 + -81x3 + (-1 * 27x3 + 3x * 27x3)) + 60x3(3x + -1)(3x + -1)(3x + -1) = 0
15x2(1 + -3x + -9x + 27x2 + 27x2 + -81x3 + (-27x3 + 81x4)) + 60x3(3x + -1)(3x + -1)(3x + -1) = 0

Combine like terms: -3x + -9x = -12x
15x2(1 + -12x + 27x2 + 27x2 + -81x3 + -27x3 + 81x4) + 60x3(3x + -1)(3x + -1)(3x + -1) = 0

Combine like terms: 27x2 + 27x2 = 54x2
15x2(1 + -12x + 54x2 + -81x3 + -27x3 + 81x4) + 60x3(3x + -1)(3x + -1)(3x + -1) = 0

Combine like terms: -81x3 + -27x3 = -108x3
15x2(1 + -12x + 54x2 + -108x3 + 81x4) + 60x3(3x + -1)(3x + -1)(3x + -1) = 0
(1 * 15x2 + -12x * 15x2 + 54x2 * 15x2 + -108x3 * 15x2 + 81x4 * 15x2) + 60x3(3x + -1)(3x + -1)(3x + -1) = 0
(15x2 + -180x3 + 810x4 + -1620x5 + 1215x6) + 60x3(3x + -1)(3x + -1)(3x + -1) = 0

Reorder the terms:
15x2 + -180x3 + 810x4 + -1620x5 + 1215x6 + 60x3(-1 + 3x)(3x + -1)(3x + -1) = 0

Reorder the terms:
15x2 + -180x3 + 810x4 + -1620x5 + 1215x6 + 60x3(-1 + 3x)(-1 + 3x)(3x + -1) = 0

Reorder the terms:
15x2 + -180x3 + 810x4 + -1620x5 + 1215x6 + 60x3(-1 + 3x)(-1 + 3x)(-1 + 3x) = 0

Multiply (-1 + 3x) * (-1 + 3x)
15x2 + -180x3 + 810x4 + -1620x5 + 1215x6 + 60x3(-1(-1 + 3x) + 3x * (-1 + 3x))(-1 + 3x) = 0
15x2 + -180x3 + 810x4 + -1620x5 + 1215x6 + 60x3((-1 * -1 + 3x * -1) + 3x * (-1 + 3x))(-1 + 3x) = 0
15x2 + -180x3 + 810x4 + -1620x5 + 1215x6 + 60x3((1 + -3x) + 3x * (-1 + 3x))(-1 + 3x) = 0
15x2 + -180x3 + 810x4 + -1620x5 + 1215x6 + 60x3(1 + -3x + (-1 * 3x + 3x * 3x))(-1 + 3x) = 0
15x2 + -180x3 + 810x4 + -1620x5 + 1215x6 + 60x3(1 + -3x + (-3x + 9x2))(-1 + 3x) = 0

Combine like terms: -3x + -3x = -6x
15x2 + -180x3 + 810x4 + -1620x5 + 1215x6 + 60x3(1 + -6x + 9x2)(-1 + 3x) = 0

Multiply (1 + -6x + 9x2) * (-1 + 3x)
15x2 + -180x3 + 810x4 + -1620x5 + 1215x6 + 60x3(1(-1 + 3x) + -6x * (-1 + 3x) + 9x2 * (-1 + 3x)) = 0
15x2 + -180x3 + 810x4 + -1620x5 + 1215x6 + 60x3((-1 * 1 + 3x * 1) + -6x * (-1 + 3x) + 9x2 * (-1 + 3x)) = 0
15x2 + -180x3 + 810x4 + -1620x5 + 1215x6 + 60x3((-1 + 3x) + -6x * (-1 + 3x) + 9x2 * (-1 + 3x)) = 0
15x2 + -180x3 + 810x4 + -1620x5 + 1215x6 + 60x3(-1 + 3x + (-1 * -6x + 3x * -6x) + 9x2 * (-1 + 3x)) = 0
15x2 + -180x3 + 810x4 + -1620x5 + 1215x6 + 60x3(-1 + 3x + (6x + -18x2) + 9x2 * (-1 + 3x)) = 0
15x2 + -180x3 + 810x4 + -1620x5 + 1215x6 + 60x3(-1 + 3x + 6x + -18x2 + (-1 * 9x2 + 3x * 9x2)) = 0
15x2 + -180x3 + 810x4 + -1620x5 + 1215x6 + 60x3(-1 + 3x + 6x + -18x2 + (-9x2 + 27x3)) = 0

Combine like terms: 3x + 6x = 9x
15x2 + -180x3 + 810x4 + -1620x5 + 1215x6 + 60x3(-1 + 9x + -18x2 + -9x2 + 27x3) = 0

Combine like terms: -18x2 + -9x2 = -27x2
15x2 + -180x3 + 810x4 + -1620x5 + 1215x6 + 60x3(-1 + 9x + -27x2 + 27x3) = 0
15x2 + -180x3 + 810x4 + -1620x5 + 1215x6 + (-1 * 60x3 + 9x * 60x3 + -27x2 * 60x3 + 27x3 * 60x3) = 0
15x2 + -180x3 + 810x4 + -1620x5 + 1215x6 + (-60x3 + 540x4 + -1620x5 + 1620x6) = 0

Reorder the terms:
15x2 + -180x3 + -60x3 + 810x4 + 540x4 + -1620x5 + -1620x5 + 1215x6 + 1620x6 = 0

Combine like terms: -180x3 + -60x3 = -240x3
15x2 + -240x3 + 810x4 + 540x4 + -1620x5 + -1620x5 + 1215x6 + 1620x6 = 0

Combine like terms: 810x4 + 540x4 = 1350x4
15x2 + -240x3 + 1350x4 + -1620x5 + -1620x5 + 1215x6 + 1620x6 = 0

Combine like terms: -1620x5 + -1620x5 = -3240x5
15x2 + -240x3 + 1350x4 + -3240x5 + 1215x6 + 1620x6 = 0

Combine like terms: 1215x6 + 1620x6 = 2835x6
15x2 + -240x3 + 1350x4 + -3240x5 + 2835x6 = 0

Solving
15x2 + -240x3 + 1350x4 + -3240x5 + 2835x6 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '15x2'.
15x2(1 + -16x + 90x2 + -216x3 + 189x4) = 0

Ignore the factor 15.

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

Subproblem 2
Set the factor '(1 + -16x + 90x2 + -216x3 + 189x4)' equal to zero and attempt to solve:

Simplifying
1 + -16x + 90x2 + -216x3 + 189x4 = 0

Solving
1 + -16x + 90x2 + -216x3 + 189x4 = 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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