Question

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

Answer 1

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} \\ (2x)/(2)=(-5)/(2) \\ \Rightarrow x=-(5)/(2) \end{gathered}`

Hence, the solution to the equation is

`x=8,\text{ x=-}(5)/(2)`