Solve 180(h-2)=n[5(n-2)]

$$180 ( h - 2 ) = n [ 5 ( n - 2 ) ]$$

Solve for h

$$h=\frac{n^{2}-2n+72}{36}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 180 by h-2.

$$180h-360=n\times 5\left(n-2\right)$$

Use the distributive property to multiply n\times 5 by n-2.

$$180h-360=5n^{2}-2n\times 5$$

Multiply -2 and 5 to get -10.

$$180h-360=5n^{2}-10n$$

Add 360 to both sides.

$$180h=5n^{2}-10n+360$$

Divide both sides by 180.

$$\frac{180h}{180}=\frac{5n^{2}-10n+360}{180}$$

Dividing by 180 undoes the multiplication by 180.

$$h=\frac{5n^{2}-10n+360}{180}$$

Divide 5n^{2}-10n+360 by 180.

$$h=\frac{n^{2}}{36}-\frac{n}{18}+2$$

Solve for n (complex solution)

$$n=\sqrt{36h-71}+1$$

$$n=-\sqrt{36h-71}+1$$

Solve for n

$$n=\sqrt{36h-71}+1$$

$$n=-\sqrt{36h-71}+1\text{, }h\geq \frac{71}{36}$$