Answer
The different question is "Find the value of $k$ for which $(2k + 4) + (k - 3) = 0.$"
The value of $k$ for which $(2k + 4) + (k - 3) = 0$ is given by $k = - \frac{1}{3}$.
The roots of the equation $(2k + 4)(k - 3) = 0$ are given by $k = -2, 3.$
Work Step by Step
To solve the equation $$(2k+4)(k-3)$$ means to find the roots of this equation, which is also equivalent to finding the values of $k$ for which $$2k+4=0\text{ or }k-3=0.$$ Therefore the different question is
"Find the value of $k$ for which $$(2k+4)+(k-3)=0."$$ We solve the equation
$$\begin{align*}
(2k+4)+(k-3)&=0\\
2k+4+k-3&=0\\
3k+1&=0\\
3k&=-1\\
k&=-\frac{1}{3}.
\end{align*}$$ We solve the equation
$$\begin{align*}
(2k+4)(k-3)&=0\\
2k+4&=0\text { or } k-3=0\\
2k&=-4\text{ or }k=3\\
k&=-2\text{ or }k=3.
\end{align*}$$ The value of $k$ for which $(2k + 4) + (k - 3) = 0$ is given by $k = - \frac{1}{3}$.
The roots of the equation $(2k + 4)(k - 3) = 0$ are given by $k = -2, 3.$
