Question
$$\frac{10x^3-18x^2-18}{9}x = 0$$
Answer
$$ x = 0 $$
Explanation
$$ \begin{aligned} \frac{10x^3-18x^2-18}{9}x &= 0&& \text{multiply ALL terms by } \color{blue}{ 9 }. \\[1 em]9 \cdot \frac{10x^3-18x^2-18}{9}x &= 9\cdot0&& \text{cancel out the denominators} \\[1 em]10x^4-18x^3-18x &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ 10x^{4}-18x^{3}-18x = 0 } $, first we need to factor our $ x $.
$$ 10x^{4}-18x^{3}-18x = x \left( 10x^{3}-18x^{2}-18 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The remaining roots can be found by solving equation $ 10x^{3}-18x^{2}-18 = 0$.
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.
This page was created using
Polynomial Equations Solver