Question
$$x\cdot3x^4+19x^3+27x^2+35x = 0$$
Answer
$$ x = 0 $$
Explanation
In order to solve $ \color{blue}{ 3x^{5}+19x^{3}+27x^{2}+35x = 0 } $, first we need to factor our $ x $.
$$ 3x^{5}+19x^{3}+27x^{2}+35x = x \left( 3x^{4}+19x^{2}+27x+35 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The remaining roots can be found by solving equation $ 3x^{4}+19x^{2}+27x+35 = 0$.
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using quartic formulas
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Polynomial Equations Solver