y^3+y^2-5y-x^2=-4

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Solution for y^3+y^2-5y-x^2=-4 equation: 


Simplifying
y3 + y2 + -5y + -1x2 = -4

Reorder the terms:
-1x2 + -5y + y2 + y3 = -4

Solving
-1x2 + -5y + y2 + y3 = -4

Solving for variable 'x'.

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

Add '5y' to each side of the equation.
-1x2 + -5y + y2 + 5y + y3 = -4 + 5y

Reorder the terms:
-1x2 + -5y + 5y + y2 + y3 = -4 + 5y

Combine like terms: -5y + 5y = 0
-1x2 + 0 + y2 + y3 = -4 + 5y
-1x2 + y2 + y3 = -4 + 5y

Add '-1y2' to each side of the equation.
-1x2 + y2 + -1y2 + y3 = -4 + 5y + -1y2

Combine like terms: y2 + -1y2 = 0
-1x2 + 0 + y3 = -4 + 5y + -1y2
-1x2 + y3 = -4 + 5y + -1y2

Add '-1y3' to each side of the equation.
-1x2 + y3 + -1y3 = -4 + 5y + -1y2 + -1y3

Combine like terms: y3 + -1y3 = 0
-1x2 + 0 = -4 + 5y + -1y2 + -1y3
-1x2 = -4 + 5y + -1y2 + -1y3

Divide each side by '-1'.
x2 = 4 + -5y + y2 + y3

Simplifying
x2 = 4 + -5y + y2 + y3

Reorder the terms:
-4 + x2 + 5y + -1y2 + -1y3 = 4 + -5y + y2 + y3 + -4 + 5y + -1y2 + -1y3

Reorder the terms:
-4 + x2 + 5y + -1y2 + -1y3 = 4 + -4 + -5y + 5y + y2 + -1y2 + y3 + -1y3

Combine like terms: 4 + -4 = 0
-4 + x2 + 5y + -1y2 + -1y3 = 0 + -5y + 5y + y2 + -1y2 + y3 + -1y3
-4 + x2 + 5y + -1y2 + -1y3 = -5y + 5y + y2 + -1y2 + y3 + -1y3

Combine like terms: -5y + 5y = 0
-4 + x2 + 5y + -1y2 + -1y3 = 0 + y2 + -1y2 + y3 + -1y3
-4 + x2 + 5y + -1y2 + -1y3 = y2 + -1y2 + y3 + -1y3

Combine like terms: y2 + -1y2 = 0
-4 + x2 + 5y + -1y2 + -1y3 = 0 + y3 + -1y3
-4 + x2 + 5y + -1y2 + -1y3 = y3 + -1y3

Combine like terms: y3 + -1y3 = 0
-4 + x2 + 5y + -1y2 + -1y3 = 0

The solution to this equation could not be determined.

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