Solve x(x+2016)=2016*1008

$$x(x+2016)=2016 \times 1008$$

Evaluate

$$2032128$$

Steps For Long Multiplication

First line up the numbers vertically and match the places from the right like this.

$$\begin{array}{c}\phantom{\times999}2016\\\underline{\times\phantom{999}1008}\\\end{array}$$

Now multiply the first number with the 1^{st} digit in 2^{nd} number to get intermediate results. That is Multiply 2016 with 8. Write the result 16128 at the end leaving 0 spaces to the right like this.

$$\begin{array}{c}\phantom{\times999}2016\\\underline{\times\phantom{999}1008}\\\phantom{\times99}16128\\\end{array}$$

Now multiply the first number with the 2^{nd} digit in 2^{nd} number to get intermediate results. That is Multiply 2016 with 0. Write the result 0 at the end leaving 1 spaces to the right like this.

$$\begin{array}{c}\phantom{\times999}2016\\\underline{\times\phantom{999}1008}\\\phantom{\times99}16128\\\phantom{\times999999}0\phantom{9}\\\end{array}$$

Now multiply the first number with the 3^{rd} digit in 2^{nd} number to get intermediate results. That is Multiply 2016 with 0. Write the result 0 at the end leaving 2 spaces to the right like this.

$$\begin{array}{c}\phantom{\times999}2016\\\underline{\times\phantom{999}1008}\\\phantom{\times99}16128\\\phantom{\times999999}0\phantom{9}\\\phantom{\times99999}0\phantom{99}\\\end{array}$$

Now multiply the first number with the 4^{th} digit in 2^{nd} number to get intermediate results. That is Multiply 2016 with 1. Write the result 2016 at the end leaving 3 spaces to the right like this.

$$\begin{array}{c}\phantom{\times999}2016\\\underline{\times\phantom{999}1008}\\\phantom{\times99}16128\\\phantom{\times999999}0\phantom{9}\\\phantom{\times99999}0\phantom{99}\\\underline{\phantom{\times}2016\phantom{999}}\\\end{array}$$

Now add the intermediate results to get final answer.

$$\begin{array}{c}\phantom{\times999}2016\\\underline{\times\phantom{999}1008}\\\phantom{\times99}16128\\\phantom{\times999999}0\phantom{9}\\\phantom{\times99999}0\phantom{99}\\\underline{\phantom{\times}2016\phantom{999}}\\\phantom{\times}2032128\end{array}$$

Factor

$$2^{9}\times 3^{4}\times 7^{2}$$