This is what I've tried:
After the first step,
But, I am not able to factorize this.
Any help would be much appreciated.
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Here is an easy way of solving $10x^2-3x-1=0$.
What we would like to do is to turn $10x^2$ into a perfect square, but just multiplying both side of the equation by $10$ will leave fractions later on (which I would like to avoid). So, instead, I'm going to multiply by $2^2\cdot10 = 40$
$$40(10x^2-3x-1)=40\cdot0$$ $$400x^2-3(40)x-40=0$$ $$20^2x^2-6(20)x-40=0$$ $$(20x)^2-6(20x)-40=0$$ let $t=20x$ $$t^2-6t-40=0$$ $$(t-10)(t+4)=0$$ $$(20x-10)(20x+4)=0$$ $$\dots$$