(4x+5xy+3y)-(3y+6x+8xy)=

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Solution for (4x+5xy+3y)-(3y+6x+8xy)= equation: 


Simplifying
(4x + 5xy + 3y) + -1(3y + 6x + 8xy) = 0

Remove parenthesis around (4x + 5xy + 3y)
4x + 5xy + 3y + -1(3y + 6x + 8xy) = 0

Reorder the terms:
4x + 5xy + 3y + -1(6x + 8xy + 3y) = 0
4x + 5xy + 3y + (6x * -1 + 8xy * -1 + 3y * -1) = 0
4x + 5xy + 3y + (-6x + -8xy + -3y) = 0

Reorder the terms:
4x + -6x + 5xy + -8xy + 3y + -3y = 0

Combine like terms: 4x + -6x = -2x
-2x + 5xy + -8xy + 3y + -3y = 0

Combine like terms: 5xy + -8xy = -3xy
-2x + -3xy + 3y + -3y = 0

Combine like terms: 3y + -3y = 0
-2x + -3xy + 0 = 0
-2x + -3xy = 0

Solving
-2x + -3xy = 0

Solving for variable 'x'.

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

Factor out the Greatest Common Factor (GCF), '-1x'.
-1x(2 + 3y) = 0

Ignore the factor -1.

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 '(2 + 3y)' equal to zero and attempt to solve:

Simplifying
2 + 3y = 0

Solving
2 + 3y = 0

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

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

Combine like terms: 2 + -2 = 0
0 + 3y = 0 + -2
3y = 0 + -2

Combine like terms: 0 + -2 = -2
3y = -2

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

Combine like terms: 3y + -3y = 0
0 = -2 + -3y

Simplifying
0 = -2 + -3y

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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