xy(y+x)=x(y^2-7)+x

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Solution for xy(y+x)=x(y^2-7)+x equation: 


Simplifying
xy(y + x) = x(y2 + -7) + x

Reorder the terms:
xy(x + y) = x(y2 + -7) + x
(x * xy + y * xy) = x(y2 + -7) + x

Reorder the terms:
(xy2 + x2y) = x(y2 + -7) + x
(xy2 + x2y) = x(y2 + -7) + x

Reorder the terms:
xy2 + x2y = x(-7 + y2) + x
xy2 + x2y = (-7 * x + y2 * x) + x
xy2 + x2y = (-7x + xy2) + x

Reorder the terms:
xy2 + x2y = -7x + x + xy2

Combine like terms: -7x + x = -6x
xy2 + x2y = -6x + xy2

Add '-1xy2' to each side of the equation.
xy2 + -1xy2 + x2y = -6x + xy2 + -1xy2

Combine like terms: xy2 + -1xy2 = 0
0 + x2y = -6x + xy2 + -1xy2
x2y = -6x + xy2 + -1xy2

Combine like terms: xy2 + -1xy2 = 0
x2y = -6x + 0
x2y = -6x

Solving
x2y = -6x

Solving for variable 'x'.

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

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(6 + xy) = 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 '(6 + xy)' equal to zero and attempt to solve:

Simplifying
6 + xy = 0

Solving
6 + xy = 0

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

Add '-6' to each side of the equation.
6 + -6 + xy = 0 + -6

Combine like terms: 6 + -6 = 0
0 + xy = 0 + -6
xy = 0 + -6

Combine like terms: 0 + -6 = -6
xy = -6

Divide each side by 'y'.
x = -6y-1

Simplifying
x = -6y-1
Solution
x = {0, -6y-1}

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