<s>[INST] Solve $10x^4-7x^2(x^2+x+1)+(x^2+x+1)^2=0$ How to solve the following equation?
$$10x^4-7x^2(x^2+x+1)+(x^2+x+1)^2=0$$

My attempt:
$$ 10x^4 - (7x^2+1)(x^2+x+1)=0$$
Thats all i can
Update
Tried to open brakets and simplify:
$$(7x^2+1)(x^2+x+1) = 7x^4+7x^3+7x^2+x^2+x+1=7x^4+7x^3+8x^2+1 $$
$$10x^4 - (7x^2+1)(x^2+x+1)= 3x^4-7x^3-8x^2-1=0 $$
 [/INST] $10x^4-7x^2(x^2+x+1)+(x^2+x+1)^2=0$
Divide by $x^4$ on both sides,
$10-\frac{7x^2(x^2+x+1)}{x^4}+\frac{(x^2+x+1)^2}{x^4}=0$
$10-7(1+\frac{1}{x}+\frac{1}{x^2})+(1+\frac{1}{x}+\frac{1}{x^2})^2=0$
Put $(1+\frac{1}{x}+\frac{1}{x^2})=t$
$10-7t+t^2=0$,solving we get $t=2,5$
when $t=2$
$1+\frac{1}{x}+\frac{1}{x^2}=2$
simplify we get,$x^2-x-1=0$.............(1)
when $t=5$
$1+\frac{1}{x}+\frac{1}{x^2}=5$
simplify we get,$4x^2-x-1=0...........(2)$
Solve (1) and (2) and get the answer.
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