Answer:
[tex]x=-\frac{2}{3}[/tex] or [tex]x=1[/tex]
Step-by-step explanation:
The given quadratic equation is [tex]3x^2-x-2=0[/tex]
You split the middle term with [tex]2x-3x[/tex] to get:
[tex]3x^2+2x-3x-2=0[/tex]
We now factor by grouping to get:
[tex]x(3x+2)-1(3x+2)=0[/tex]
Factor again to get:
[tex](3x+2)(x-1)=0[/tex]
Apply the zero product principle to get:
[tex](3x+2)=0[/tex] or [tex](x-1)=0[/tex]
This implies that:
[tex]x=-\frac{2}{3}[/tex] or [tex]x=1[/tex]
