Question

Solve the given equation.

$\mathbf{6}\mathit{k}\left(k+2\right)\mathbf{=}\mathbf{6}\left(k^2+4\right)$

Short answer

$\mathit{k}\mathbf{=}\mathbf{2}$is the solution of the given equation.

Step-by-step solution

Step 1. Define an equation.

In mathematics, an equation is a statement that asserts the equality of two expressions, which are connected by the equal sign $"="$.

Step 2. Define the power of a product rule.

Power of a product rule states that if the two exponents of the same base are multiplied then the exponents are added and base remains the same.

$a^m.a^n=a^{m+n}$

Where,$a$ is any non-zero real number.

Solve the equation, 6k(k+2)=6(k2+4).

Use the power of a product rule to solve the equation.

$\begin{array}{c}6k\left(k+2\right)=6\left(k^2+4\right)\\ 6k\left(k\right)+6k\left(2\right)=6\left(k^2\right)+6\left(4\right)\\ 6k^2+12k=6k^2+24\\ 6k^2+12k-6k^2=24\\ 12k=24\\ k=\frac{24}{12}\\ k=2\end{array}$

Therefore,$k=2$is the solution of the given equation.