Question

In the following exercises, solve.

$(x+6)(x-3)=-8$

Short answer

Answer is$x=2,x=-5$

Step-by-step solution

Step 1. Given

The equation is$(x+6)(x-3)=-8$

Step 2. Simplify the equation

$$\begin{gathered} (x+6)(x-3)=-8 \\ {x}^2+3x-18=-8 \\ {x}^2+3x-10=0 \\ {x}^2+5x-2x-10=0 \\ x(x+5)-2(x+5)=0 \\ (x+5)(x-2)=0 \end{gathered}$$

So,

$$\begin{gathered} x+5=0 \\ x=-5 \end{gathered}$$

and

$$\begin{gathered} x-2=0 \\ x=2 \end{gathered}$$

Step 3. Check both the values

Put $x=-5$in the original equation

$$\begin{gathered} (x+6)(x-3)=-8 \\ (-5+6)(-5-3)=-8 \\ 1\times -8=-8 \\ -8=-8 \end{gathered}$$

True

Now put $x=2$in the original equation,

$$\begin{gathered} (x+6)(x-3)=-8 \\ (2+6)(2-3)=-8 \\ 8\times -1=-8 \\ -8=-8 \end{gathered}$$

True

Step 4. Required answer

Answer is$x=2,x=-5$