Question

Solve 5x(x-6)(4x+9)=0

Answer 1

Greetings and Happy Holidays!

Solve for x.

`5x(x-6)(4x+9)=0`

Distribute the parenthesis:

`5x(x-6)(4x+9)=0`


`(5x^2-30x)(4x+9)=0`


`(20x^3-120x^2)+(45x^2-270x)=0`

Combine like terms:

`20x^3-75x^2-270x=0`

Factor out GCF (5x):

`5x(4x^2-15x-54)=0`

Factor the Complex Trinomial:

`5x(4x^2+9x-24x-54)=0`


`5x(x(4x+9)-6(4x-9))=0`


`5x((4x+9)(x-6))=0`

Set Factors to Equal 0:

`5x=0`


`x=0`

or


`4x+9=0`


`4x=-9`


`x=(-9)/(4)`

or


`x-6=0`


`x=6`

The Answers Are:

`\boxed{x=0} \\ \boxed{x= (-9)/(4)} \\ \boxed{x=6}`

I hope this helped!
-Benjamin