Solve the following equation: (3(x-6) - 81)/4x = 0
The first step is to realise that a trivial solution of x is x = 0, which can be determined from the '4x' denominator. Now zooming in on the numerator and expanding gives us '3x^2 - 18 - 81'. Looking at the coefficients a factor of 3 can be taken out, leaving us with 'x^2 - 6 - 27'.Thinking of numbers that multiply to -27 and add to -6, the 27 immediately highlights that these will be some combination of 9 and 3. It is now apparent that the solution to this problem is in the form of (x-9)(x+3), giving x = 9, -3 or 0
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