Question
$$(x^2+x+1)(x^2+x+3) = 4$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} (x^2+x+1)(x^2+x+3) &= 4&& \text{simplify left side} \\[1 em]x^4+2x^3+5x^2+4x+3 &= 4&& \text{move all terms to the left hand side } \\[1 em]x^4+2x^3+5x^2+4x+3-4 &= 0&& \text{simplify left side} \\[1 em]x^4+2x^3+5x^2+4x-1 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using quartic formulas
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Equations Solver