Question
$$4x(1-x)^2 = \frac{3}{10}$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 4x(1-x)^2 &= \frac{3}{10}&& \text{multiply ALL terms by } \color{blue}{ 10 }. \\[1 em]104x(1-x)^2 &= 10\cdot\frac{3}{10}&& \text{cancel out the denominators} \\[1 em]10\cdot4x(1-x)^2 &= 3&& \text{simplify left side} \\[1 em]40x(1-x)^2 &= 3&& \\[1 em]40x(1-2x+x^2) &= 3&& \\[1 em]40x-80x^2+40x^3 &= 3&& \\[1 em]40x^3-80x^2+40x &= 3&& \text{move all terms to the left hand side } \\[1 em]40x^3-80x^2+40x-3 &= 0&& \\[1 em] \end{aligned} $$
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