((5x-1)(3x^2-12x))*((5x-1)(x-4))=0

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Solution for ((5x-1)(3x^2-12x))*((5x-1)(x-4))=0 equation: 


Simplifying
((5x + -1)(3x2 + -12x))((5x + -1)(x + -4)) = 0

Reorder the terms:
((-1 + 5x)(3x2 + -12x))((5x + -1)(x + -4)) = 0

Reorder the terms:
((-1 + 5x)(-12x + 3x2))((5x + -1)(x + -4)) = 0

Multiply (-1 + 5x) * (-12x + 3x2)
((-1(-12x + 3x2) + 5x * (-12x + 3x2)))((5x + -1)(x + -4)) = 0
(((-12x * -1 + 3x2 * -1) + 5x * (-12x + 3x2)))((5x + -1)(x + -4)) = 0
(((12x + -3x2) + 5x * (-12x + 3x2)))((5x + -1)(x + -4)) = 0
((12x + -3x2 + (-12x * 5x + 3x2 * 5x)))((5x + -1)(x + -4)) = 0
((12x + -3x2 + (-60x2 + 15x3)))((5x + -1)(x + -4)) = 0

Combine like terms: -3x2 + -60x2 = -63x2
((12x + -63x2 + 15x3))((5x + -1)(x + -4)) = 0

Reorder the terms:
(12x + -63x2 + 15x3)((-1 + 5x)(x + -4)) = 0

Reorder the terms:
(12x + -63x2 + 15x3)((-1 + 5x)(-4 + x)) = 0

Multiply (-1 + 5x) * (-4 + x)
(12x + -63x2 + 15x3)((-1(-4 + x) + 5x * (-4 + x))) = 0
(12x + -63x2 + 15x3)(((-4 * -1 + x * -1) + 5x * (-4 + x))) = 0
(12x + -63x2 + 15x3)(((4 + -1x) + 5x * (-4 + x))) = 0
(12x + -63x2 + 15x3)((4 + -1x + (-4 * 5x + x * 5x))) = 0
(12x + -63x2 + 15x3)((4 + -1x + (-20x + 5x2))) = 0

Combine like terms: -1x + -20x = -21x
(12x + -63x2 + 15x3)((4 + -21x + 5x2)) = 0

Multiply (12x + -63x2 + 15x3) * (4 + -21x + 5x2)
(12x * (4 + -21x + 5x2) + -63x2 * (4 + -21x + 5x2) + 15x3 * (4 + -21x + 5x2)) = 0
((4 * 12x + -21x * 12x + 5x2 * 12x) + -63x2 * (4 + -21x + 5x2) + 15x3 * (4 + -21x + 5x2)) = 0
((48x + -252x2 + 60x3) + -63x2 * (4 + -21x + 5x2) + 15x3 * (4 + -21x + 5x2)) = 0
(48x + -252x2 + 60x3 + (4 * -63x2 + -21x * -63x2 + 5x2 * -63x2) + 15x3 * (4 + -21x + 5x2)) = 0
(48x + -252x2 + 60x3 + (-252x2 + 1323x3 + -315x4) + 15x3 * (4 + -21x + 5x2)) = 0
(48x + -252x2 + 60x3 + -252x2 + 1323x3 + -315x4 + (4 * 15x3 + -21x * 15x3 + 5x2 * 15x3)) = 0
(48x + -252x2 + 60x3 + -252x2 + 1323x3 + -315x4 + (60x3 + -315x4 + 75x5)) = 0

Reorder the terms:
(48x + -252x2 + -252x2 + 60x3 + 1323x3 + 60x3 + -315x4 + -315x4 + 75x5) = 0

Combine like terms: -252x2 + -252x2 = -504x2
(48x + -504x2 + 60x3 + 1323x3 + 60x3 + -315x4 + -315x4 + 75x5) = 0

Combine like terms: 60x3 + 1323x3 = 1383x3
(48x + -504x2 + 1383x3 + 60x3 + -315x4 + -315x4 + 75x5) = 0

Combine like terms: 1383x3 + 60x3 = 1443x3
(48x + -504x2 + 1443x3 + -315x4 + -315x4 + 75x5) = 0

Combine like terms: -315x4 + -315x4 = -630x4
(48x + -504x2 + 1443x3 + -630x4 + 75x5) = 0

Solving
48x + -504x2 + 1443x3 + -630x4 + 75x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(16 + -168x + 481x2 + -210x3 + 25x4) = 0

Ignore the factor 3.

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 '(16 + -168x + 481x2 + -210x3 + 25x4)' equal to zero and attempt to solve:

Simplifying
16 + -168x + 481x2 + -210x3 + 25x4 = 0

Solving
16 + -168x + 481x2 + -210x3 + 25x4 = 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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