Question
$$(x^2-4x+3)(x^2-4x+4) = 20$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} (x^2-4x+3)(x^2-4x+4) &= 20&& \text{simplify left side} \\[1 em]x^4-8x^3+23x^2-28x+12 &= 20&& \text{move all terms to the left hand side } \\[1 em]x^4-8x^3+23x^2-28x+12-20 &= 0&& \text{simplify left side} \\[1 em]x^4-8x^3+23x^2-28x-8 &= 0&& \\[1 em] \end{aligned} $$
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