4x^3y+6x^27-2x=2x(2x^2y+3xy-1)

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Solution for 4x^3y+6x^27-2x=2x(2x^2y+3xy-1) equation: 


Simplifying
4x3y + 6x27 + -2x = 2x(2x2y + 3xy + -1)

Reorder the terms:
-2x + 4x3y + 6x27 = 2x(2x2y + 3xy + -1)

Reorder the terms:
-2x + 4x3y + 6x27 = 2x(-1 + 3xy + 2x2y)
-2x + 4x3y + 6x27 = (-1 * 2x + 3xy * 2x + 2x2y * 2x)
-2x + 4x3y + 6x27 = (-2x + 6x2y + 4x3y)

Add '2x' to each side of the equation.
-2x + 4x3y + 2x + 6x27 = -2x + 6x2y + 2x + 4x3y

Reorder the terms:
-2x + 2x + 4x3y + 6x27 = -2x + 6x2y + 2x + 4x3y

Combine like terms: -2x + 2x = 0
0 + 4x3y + 6x27 = -2x + 6x2y + 2x + 4x3y
4x3y + 6x27 = -2x + 6x2y + 2x + 4x3y

Reorder the terms:
4x3y + 6x27 = -2x + 2x + 6x2y + 4x3y

Combine like terms: -2x + 2x = 0
4x3y + 6x27 = 0 + 6x2y + 4x3y
4x3y + 6x27 = 6x2y + 4x3y

Add '-4x3y' to each side of the equation.
4x3y + -4x3y + 6x27 = 6x2y + 4x3y + -4x3y

Combine like terms: 4x3y + -4x3y = 0
0 + 6x27 = 6x2y + 4x3y + -4x3y
6x27 = 6x2y + 4x3y + -4x3y

Combine like terms: 4x3y + -4x3y = 0
6x27 = 6x2y + 0
6x27 = 6x2y

Solving
6x27 = 6x2y

Solving for variable 'x'.

Reorder the terms:
-6x2y + 6x27 = 6x2y + -6x2y

Combine like terms: 6x2y + -6x2y = 0
-6x2y + 6x27 = 0

Factor out the Greatest Common Factor (GCF), '6x2'.
6x2(-1y + x25) = 0

Ignore the factor 6.

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 '(-1y + x25)' equal to zero and attempt to solve:

Simplifying
-1y + x25 = 0

Reorder the terms:
x25 + -1y = 0

Solving
x25 + -1y = 0

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

Add 'y' to each side of the equation.
x25 + -1y + y = 0 + y

Combine like terms: -1y + y = 0
x25 + 0 = 0 + y
x25 = 0 + y
Remove the zero:
x25 = y

Simplifying
x25 = y

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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