Respuesta :

BenjaminG123
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

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