Question

How do you solve `(2x+8)(3x-6)=0` using any method?

Answer 1

`x=-4 or x=2`

Explanation:

Expand the equation from the brackets

`(2x+8)(3x-6)=0`
`(color(red)(2x)`+8)(`color(red)(3x)-6)` Multiply the highest power of `x` first
`(color(red)(2x)`+8)(3x`color(red)(-6)`) Next multiply by the next highest power

(2x`color(blue)(+8`)(`color(blue)(3x)`-6) Multiply by the highest power
(2x`color(blue)(+8`)(3x`color(blue)(-6)`) Multiply by next highest power.

Therefore,
`6x^2-12x+24x-48=0`
`6x^2+12x-48`=0 ------------------Divide the equation by 6
`x^2+2x-8=0` --------------------------Simplify the equation
`(x+4)(x-2)=0`
`x+4=0 or x-2=0`
`x=-4 or x=2`