Question 67132
4x^2 - 9 = 0
This form is called "difference of squares".
This is the way it factors: 
a^2-b^2=(a-b)(a+b)
In your problem a=2x and b=3
So you factor the left side to get:
(2x-3)(2x+3)=0
Since the product is zero one of the factors must be zero.
So: 2x-3=0 or 2x+3=0
Then x=3/2 or x=-3/2
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That is the standard way to proceed with your problem.
Cheers,
Stan H.