Question

In the following exercises, solve.

$q^3+3q^2+2q=0$

Short answer

Answer is$q=0,q=-1,q=-2$

Step-by-step solution

Step 1. Given

The equation is $q^3+3q^2+2q=0$

Step 2. Simplify the equation

$$\begin{gathered} q^3+3q^2+2q=0 \\ q(q^2+3q+2)=0 \\ q(q^2+2q+q+2)=0 \\ q\left(q\right(q+2)+1(q+2\left)\right)=0 \\ q(q+2)(q+1)=0 \end{gathered}$$

So,

$q=0$

and

$$\begin{gathered} q+2=0 \\ q=-2 \end{gathered}$$

and

$$\begin{gathered} q+1=0 \\ q=-1 \end{gathered}$$

Step 3. Check all the values

Put $q=0$in the original equation,

$$\begin{gathered} q^3+3q^2+2q=0 \\ {0}^3+3{\left(0\right)}^2+2\left(0\right)=0 \\ 0=0 \end{gathered}$$

True

Now put $q=-2$in original equation,

$$\begin{gathered} q^3+3q^2+2q=0 \\ {(-2)}^3+3{(-2)}^2+2(-2)=0 \\ -8+12-4=0 \\ 0=0 \end{gathered}$$

True

Now put $q=-1$in the original equation,

$$\begin{gathered} q^3+3q^2+2q=0 \\ {(-1)}^3+3{(-1)}^2+2(-1)=0 \\ -1+3-2=0 \\ 0=0 \end{gathered}$$

True

Step 4. Required answer

Answer is$q=0,q=-2,q=-1$