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4xy+2x+2=-2y
Subtract 2y from both sides. Anything subtracted from zero gives its negation.
4xy+2x=-2y-2
Subtract 2 from both sides.
\left(4y+2\right)x=-2y-2
Combine all terms containing x.
\frac{\left(4y+2\right)x}{4y+2}=\frac{-2y-2}{4y+2}
Divide both sides by 4y+2.
x=\frac{-2y-2}{4y+2}
Dividing by 4y+2 undoes the multiplication by 4y+2.
x=-\frac{y+1}{2y+1}
Divide -2y-2 by 4y+2.
4xy+2y+2=-2x
Subtract 2x from both sides. Anything subtracted from zero gives its negation.
4xy+2y=-2x-2
Subtract 2 from both sides.
\left(4x+2\right)y=-2x-2
Combine all terms containing y.
\frac{\left(4x+2\right)y}{4x+2}=\frac{-2x-2}{4x+2}
Divide both sides by 4x+2.
y=\frac{-2x-2}{4x+2}
Dividing by 4x+2 undoes the multiplication by 4x+2.
y=-\frac{x+1}{2x+1}
Divide -2x-2 by 4x+2.