Solve x(6-x)=216/25

$$x(6-x)= \frac{ 216 }{ 25 }$$

Evaluate

$$\frac{216}{25}=8.64$$

Steps For Long Division Method

Use the 1^{st} digit 2 from dividend 216

$$\begin{array}{l}\phantom{25)}\phantom{1}\\25\overline{)216}\\\end{array}$$

Since 2 is less than 25, use the next digit 1 from dividend 216 and add 0 to the quotient

$$\begin{array}{l}\phantom{25)}0\phantom{2}\\25\overline{)216}\\\end{array}$$

Use the 2^{nd} digit 1 from dividend 216

$$\begin{array}{l}\phantom{25)}0\phantom{3}\\25\overline{)216}\\\end{array}$$

Since 21 is less than 25, use the next digit 6 from dividend 216 and add 0 to the quotient

$$\begin{array}{l}\phantom{25)}00\phantom{4}\\25\overline{)216}\\\end{array}$$

Use the 3^{rd} digit 6 from dividend 216

$$\begin{array}{l}\phantom{25)}00\phantom{5}\\25\overline{)216}\\\end{array}$$

Find closest multiple of 25 to 216. We see that 8 \times 25 = 200 is the nearest. Now subtract 200 from 216 to get reminder 16. Add 8 to quotient.

$$\begin{array}{l}\phantom{25)}008\phantom{6}\\25\overline{)216}\\\phantom{25)}\underline{\phantom{}200\phantom{}}\\\phantom{25)9}16\\\end{array}$$

Since 16 is less than 25, stop the division. The reminder is 16. The topmost line 008 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 8.

$$\text{Quotient: }8 \text{Reminder: }16$$

Factor

$$\frac{2 ^ {3} \cdot 3 ^ {3}}{5 ^ {2}} = 8\frac{16}{25} = 8.64$$