Factorise 6x^2 + 7x - 3=0

In order to solve the equation, we need to find a way to break the '7x' term in the middle that allows factorisation. We also need to consider the fact that the last term '-3x' has a minus sign. This broadens the possibilities of combinations that allow for factorisation.
After various attempts, we realise that 7x = -2x + 9x. Plugging this into the initial equation, we obtain 6x^2 - 2x + 9x - 3 = 0. After the initial factorisation, we obtain 2x(3x-1) + 3(3x-1)=0. This can be written as (2x+3)(3x-1)=0.
Qed. This means that the problem is solved.