x^4+x^2=x^2(y-7)

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Solution for x^4+x^2=x^2(y-7) equation: 


Simplifying
x4 + x2 = x2(y + -7)

Reorder the terms:
x2 + x4 = x2(y + -7)

Reorder the terms:
x2 + x4 = x2(-7 + y)
x2 + x4 = (-7 * x2 + y * x2)
x2 + x4 = (-7x2 + x2y)

Solving
x2 + x4 = -7x2 + x2y

Solving for variable 'x'.

Reorder the terms:
x2 + 7x2 + -1x2y + x4 = -7x2 + x2y + 7x2 + -1x2y

Combine like terms: x2 + 7x2 = 8x2
8x2 + -1x2y + x4 = -7x2 + x2y + 7x2 + -1x2y

Reorder the terms:
8x2 + -1x2y + x4 = -7x2 + 7x2 + x2y + -1x2y

Combine like terms: -7x2 + 7x2 = 0
8x2 + -1x2y + x4 = 0 + x2y + -1x2y
8x2 + -1x2y + x4 = x2y + -1x2y

Combine like terms: x2y + -1x2y = 0
8x2 + -1x2y + x4 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(8 + -1y + x2) = 0


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 '(8 + -1y + x2)' equal to zero and attempt to solve:

Simplifying
8 + -1y + x2 = 0

Reorder the terms:
8 + x2 + -1y = 0

Solving
8 + x2 + -1y = 0

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

Add '-8' to each side of the equation.
8 + x2 + -8 + -1y = 0 + -8

Reorder the terms:
8 + -8 + x2 + -1y = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x2 + -1y = 0 + -8
x2 + -1y = 0 + -8

Combine like terms: 0 + -8 = -8
x2 + -1y = -8

Add 'y' to each side of the equation.
x2 + -1y + y = -8 + y

Combine like terms: -1y + y = 0
x2 + 0 = -8 + y
x2 = -8 + y

Simplifying
x2 = -8 + 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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