Question

Find the real solutions of the equation$x^2+8x+12=0$ by factoring.

Short answer

The real solution of the equation is $x=-2\text{and}x=-6$.

Step-by-step solution

Step 1. Factorized the given quadratic equation

$$\begin{gathered} x^2+8x+12=0....\left(\text{Given}\right) \\ {x}^2+\left(2x+6x\right)+12=0 \\ x\left(x+2\right)+6\left(x+2\right)=0....\left(\text{Factorized}\right) \\ \left(x+2\right)\left(x+6\right)=0....\left(1\right) \end{gathered}$$

Step 2. Further simplifying (1).

$$\begin{gathered} \left(x+2\right)\left(x+6\right)=0....\left(\text{From}\left(1\right)\right) \\ x+2=0\text{or}x+6=0 \\ x=-2\text{or}x=-6 \end{gathered}$$

Step 3. DESCRIPTION OF STEPS.

From the obtained values, the real solution of the equation is $x=-2\text{and}x=-6$.