(x^2+3x)=(x^2-xy)

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Solution for (x^2+3x)=(x^2-xy) equation: 


Simplifying
(x2 + 3x) = (x2 + -1xy)

Reorder the terms:
(3x + x2) = (x2 + -1xy)

Remove parenthesis around (3x + x2)
3x + x2 = (x2 + -1xy)

Reorder the terms:
3x + x2 = (-1xy + x2)

Remove parenthesis around (-1xy + x2)
3x + x2 = -1xy + x2

Add '-1x2' to each side of the equation.
3x + x2 + -1x2 = -1xy + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
3x + 0 = -1xy + x2 + -1x2
3x = -1xy + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
3x = -1xy + 0
3x = -1xy

Solving
3x = -1xy

Solving for variable 'x'.

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

Add 'xy' to each side of the equation.
3x + xy = -1xy + xy

Combine like terms: -1xy + xy = 0
3x + xy = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(3 + y) = 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 '(3 + y)' equal to zero and attempt to solve:

Simplifying
3 + y = 0

Solving
3 + 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 + -3 + y = 0 + -3

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

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

Add '-1y' to each side of the equation.
y + -1y = -3 + -1y

Combine like terms: y + -1y = 0
0 = -3 + -1y

Simplifying
0 = -3 + -1y

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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