Question

(x-8)(2x+5)=0 solve the equation

Answer 1

Solution:

Given the equation:

$(x-8)(2x+5)=0$

To solve the equation, we use the zero factor principle.

From the zero factor principle, we have

$\begin{gathered} When\text{ } \\ ab=0 \\ \Rightarrow a=0\text{ or b=0} \end{gathered}$

Thus, we have

$\begin{gathered} x-8=0\text{ or 2x+5 =0} \\ when \\ x-8=0 \\ add\text{ 8 to both sides of the equation} \\ x-8+8=0+8 \\ \Rightarrow x=8 \\ when \\ 2x+5=0 \\ add\text{ -5 to both sides of the equation,} \\ 2x+5-5=0-5 \\ \Rightarrow2x=-5 \\ divide\text{ both sides by the coeffient of x, which is 2} \\ \frac{2x}{2}=\frac{-5}{2} \\ \Rightarrow x=-\frac{5}{2} \end{gathered}$

Hence, the solution to the equation is

$x=8,\text{ x=-}\frac{5}{2}$