MathNet 2021 — Part 06 Question 21

Let $a,b,c$ be nonnegative real numbers such that
$$
2(a^2+b^2+c^2)+3(ab+bc+ca)=5(a+b+c).
$$
Prove that $4(a^2+b^2+c^2)+2(ab+bc+ca)+7abc\le25$.