Question

How do you solve $\left( {n + 2} \right)\left( {2n + 5} \right) = 0$by factoring ?

Answer 1

Hint:We know that the given equation $\left( {n + 2} \right)\left( {2n + 5} \right) = 0$is already in the factor form. This is because Two factors $\left( {n + 2} \right)$ and $\left( {2n + 5} \right)$ are already given. Therefore, there are two possible solutions for this equation which we will find out by applying simple rules of solving a linear equation with one variable.

Complete step by step answer:
We are given the equation $\left( {n + 2} \right)\left( {2n + 5} \right) = 0$. As there are two factors, two solutions are possible for this equation: $\left( {n + 2} \right) = 0$or $\left( {2n + 5} \right) = 0$. Let us first solve the equation $\left( {n + 2} \right) = 0$.
$n + 2 = 0$
Here, the digit 2 is added to variable $n$ on the left hand side of the equation. Therefore, we need to remove 2 from the left hand side. We can do this by subtracting 2 from both the sides of the equation.
$n + 2 - 2 = 0 - 2 \\
\Rightarrow n = - 2 \\ $
Now, we will solve for the second factor which is $\left( {2n + 5} \right) = 0$
$2n + 5 = 0$
Here, we will first consider the digit 5 which is added to $2n$ on the left hand side of the equation. To remove this, we will subtract 5 from both the sides of the equation.
$2n + 5 - 5 = 0 - 5 \\
\Rightarrow 2n = - 5 \\ $
We can see that there is still one digit 2 which is multiplied with the variable $n$. Therefore, we need to remove this to find the solution. For this, we will divide both the sides of the equation by 2.
$\dfrac{{2n}}{2} = \dfrac{{ - 5}}{2} \\
\therefore n = \dfrac{{ - 5}}{2} \\ $
Thus, the solution for the given equation $\left( {n + 2} \right)\left( {2n + 5} \right) = 0$ are $ - 2$ and $ - \dfrac{5}{2}$.

Note:It is important to keep in mind that while solving a simple equation, we need to think of the equation as a balance. Thus, if we do something to one side of the equation, we must do the same thing to the other side. Doing the same thing to both sides of the equation keeps the equation balanced.