Solve (nY-1)+4Y=-40/56

$$( n Y - 1 ) + 4 Y = \frac { - 40 } { 56 }$$

Solve for Y

$$Y=\frac{2}{7\left(n+4\right)}$$

$$n\neq -4$$

Steps for Solving Linear Equation

Reduce the fraction \frac{-40}{56} to lowest terms by extracting and canceling out 8.

$$nY-1+4Y=-\frac{5}{7}$$

Add 1 to both sides.

$$nY+4Y=-\frac{5}{7}+1$$

Add -\frac{5}{7} and 1 to get \frac{2}{7}.

$$nY+4Y=\frac{2}{7}$$

Combine all terms containing Y.

$$\left(n+4\right)Y=\frac{2}{7}$$

Divide both sides by n+4.

$$\frac{\left(n+4\right)Y}{n+4}=\frac{\frac{2}{7}}{n+4}$$

Dividing by n+4 undoes the multiplication by n+4.

$$Y=\frac{\frac{2}{7}}{n+4}$$

Divide \frac{2}{7} by n+4.

$$Y=\frac{2}{7\left(n+4\right)}$$

Solve for n

$$n=-4+\frac{2}{7Y}$$

$$Y\neq 0$$

Steps for Solving Linear Equation

Reduce the fraction \frac{-40}{56} to lowest terms by extracting and canceling out 8.

$$nY-1+4Y=-\frac{5}{7}$$

Add 1 to both sides.

$$nY+4Y=-\frac{5}{7}+1$$

Add -\frac{5}{7} and 1 to get \frac{2}{7}.

$$nY+4Y=\frac{2}{7}$$

Subtract 4Y from both sides.

$$nY=\frac{2}{7}-4Y$$

The equation is in standard form.

$$Yn=\frac{2}{7}-4Y$$

Divide both sides by Y.

$$\frac{Yn}{Y}=\frac{\frac{2}{7}-4Y}{Y}$$

Dividing by Y undoes the multiplication by Y.

$$n=\frac{\frac{2}{7}-4Y}{Y}$$

Divide \frac{2}{7}-4Y by Y.

$$n=-4+\frac{2}{7Y}$$