somebody please teach me to complete the square

hello

could you please be that nice to teach me how to complete the square, step by step, i think i understand most of it, except when it comes to factorize, i'm being taught about ellipses and hyperbolas and i'm having a very hard time because i don't know how to complete the square

for example how would you solve this excercise

4x^2+3y^2+8x-6y=0

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this is whow i would do it

2 (2x^2 +4+4) 3(y^2-2y+2) = 0

ok I give up, i don't know how to do it, please help me

thank you.