Greetings and Happy Holidays!
Solve for x.
[tex]5x(x-6)(4x+9)=0[/tex]
Distribute the parenthesis:
[tex]5x(x-6)(4x+9)=0[/tex]
[tex](5x^2-30x)(4x+9)=0[/tex]
[tex](20x^3-120x^2)+(45x^2-270x)=0[/tex]
Combine like terms:
[tex]20x^3-75x^2-270x=0[/tex]
Factor out GCF (5x):
[tex]5x(4x^2-15x-54)=0[/tex]
Factor the Complex Trinomial:
[tex]5x(4x^2+9x-24x-54)=0[/tex]
[tex]5x(x(4x+9)-6(4x-9))=0[/tex]
[tex]5x((4x+9)(x-6))=0[/tex]
Set Factors to Equal 0:
[tex]5x=0[/tex]
[tex]x=0[/tex]
or
[tex]4x+9=0[/tex]
[tex]4x=-9[/tex]
[tex]x=\frac{-9}{4}[/tex]
or
[tex]x-6=0[/tex]
[tex]x=6[/tex]
The Answers Are:
[tex]\boxed{x=0} \\ \boxed{x= \frac{-9}{4}} \\ \boxed{x=6} [/tex]
I hope this helped!
-Benjamin
