Chapter 8.2, Problem 36PPS

To determine

To solve the given equation.

Answer to Problem 36PPS

  $k=-6$

Explanation of Solution

Given:

  $2k\left(-3k+4\right)+6\left(k^2+10\right)=k\left(4k+8\right)-2k\left(2k+5\right)$

Calculation:

Solving the given equation,

  $\Rightarrow 2k\left(-3k+4\right)+6\left(k^2+10\right)=k\left(4k+8\right)-2k\left(2k+5\right)$

  $\Rightarrow -6k^2+8k+6k^2+60=4k^2+8k-4k^2-10k$   [Solving the brackets]

  $\Rightarrow -6k^2+6k^2+8k+60=4k^2-4k^2+8k-10k$   [Rearranging the terms]

  $\Rightarrow 8k+60=-2k$  [Solving both sides]

  $\Rightarrow 8k+60+2k=0$  [Solving both sides]

  $\Rightarrow 8k+2k+60=0$  [Rearranging the terms]

  $\Rightarrow 10k+60=0$

  $\begin{array}{l}\Rightarrow 10k=-60\\ \Rightarrow k=-\frac{60}{10}\\ \Rightarrow k=-6\end{array}$

Conclusion:

Therefore, the value of $k=-6$ .