y(x)=2lnx-4x^4+3x

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Solution for y(x)=2lnx-4x^4+3x equation: 


Simplifying
y(x) = 2lnx + -4x4 + 3x

Multiply y * x
xy = 2lnx + -4x4 + 3x

Reorder the terms:
xy = 2lnx + 3x + -4x4

Solving
xy = 2lnx + 3x + -4x4

Solving for variable 'x'.

Reorder the terms:
-2lnx + -3x + xy + 4x4 = 2lnx + 3x + -4x4 + -2lnx + -3x + 4x4

Reorder the terms:
-2lnx + -3x + xy + 4x4 = 2lnx + -2lnx + 3x + -3x + -4x4 + 4x4

Combine like terms: 2lnx + -2lnx = 0
-2lnx + -3x + xy + 4x4 = 0 + 3x + -3x + -4x4 + 4x4
-2lnx + -3x + xy + 4x4 = 3x + -3x + -4x4 + 4x4

Combine like terms: 3x + -3x = 0
-2lnx + -3x + xy + 4x4 = 0 + -4x4 + 4x4
-2lnx + -3x + xy + 4x4 = -4x4 + 4x4

Combine like terms: -4x4 + 4x4 = 0
-2lnx + -3x + xy + 4x4 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-2ln + -3 + y + 4x3) = 0


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 '(-2ln + -3 + y + 4x3)' equal to zero and attempt to solve:

Simplifying
-2ln + -3 + y + 4x3 = 0

Reorder the terms:
-3 + -2ln + 4x3 + y = 0

Solving
-3 + -2ln + 4x3 + y = 0

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

Add '3' to each side of the equation.
-3 + -2ln + 4x3 + 3 + y = 0 + 3

Reorder the terms:
-3 + 3 + -2ln + 4x3 + y = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2ln + 4x3 + y = 0 + 3
-2ln + 4x3 + y = 0 + 3

Combine like terms: 0 + 3 = 3
-2ln + 4x3 + y = 3

Add '2ln' to each side of the equation.
-2ln + 4x3 + 2ln + y = 3 + 2ln

Reorder the terms:
-2ln + 2ln + 4x3 + y = 3 + 2ln

Combine like terms: -2ln + 2ln = 0
0 + 4x3 + y = 3 + 2ln
4x3 + y = 3 + 2ln

Add '-1y' to each side of the equation.
4x3 + y + -1y = 3 + 2ln + -1y

Combine like terms: y + -1y = 0
4x3 + 0 = 3 + 2ln + -1y
4x3 = 3 + 2ln + -1y

Divide each side by '4'.
x3 = 0.75 + 0.5ln + -0.25y

Simplifying
x3 = 0.75 + 0.5ln + -0.25y

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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