Answer:
[tex]\Large \boxed{x=\frac{-9}{13} \ \ \mathrm{or} \ \ x = -1}}[/tex]
Step-by-step explanation:
[tex]13x^2 + 13x + 9x + 9 = 0[/tex]
Factor the expression.
[tex]13x(x+1)+9(x+1)=0[/tex]
Take (x + 1) as a common factor.
[tex](13x+9)(x+1)=0[/tex]
Set factors equal to 0.
First possibility:
[tex]13x + 9 = 0[/tex]
[tex]13x=-9[/tex]
[tex]\displaystyle x=\frac{-9}{13}[/tex]
Second possibility:
[tex]x+1=0[/tex]
[tex]x=-1[/tex]
