Recall that:
[tex]ab=0[/tex]
if and only if:
[tex]a=0\text{ or b=0.}[/tex]
Therefore:
[tex](x-4)(2x+5)=0,[/tex]
if and only if:
[tex]x-4=\text{ or }2x+5=0.[/tex]
Solving each equation for x, we get:
[tex]\begin{gathered} x-4+4=0+4, \\ x=4, \\ 2x+5=0, \\ 2x=-5, \\ x=-\frac{5}{2}. \end{gathered}[/tex]
Answer:
[tex]x=4,\text{ or }x=-\frac{5}{2}.[/tex]
