A level maths help pure

I don't understand how to 'equating terms in x^2' works with partial fractions and repeated factors. I can do every single step before the equating with confidence but I don't understand how they decide which letters will add up to the coefficient of the X^2 in the quadratic, I feel like there is a step (or several missing). I am stuck on question 6:

https://www.physicsandmathstutor.com/pdf-pages/?pdf=https%3A%2F%2Factiveteach-prod.resource.pearson-intl.com%2Fr00%2Fr0069%2Fr006952%2Fr00695252%2Fcurrent%2Falevelsb_p2_ex1e.pdf

Reply 1

Skiwi

Original post by Idk131

Because LHS=RHS the coefficients in front of each term must be the same. So as on the LHS x^2 has a coefficient of 10 then the coefficient of the x^2 term on the RHS must also be 10. If you expand the RHS completely you should see that you have several x^2 terms, so you know that if you add these up they must equal 10.