$$x(x+1)(2x+1) = 12$$
Answer
$$ \begin{matrix}x_1 = 1.36297 & x_2 = -1.43149+1.53395i & x_3 = -1.43149-1.53395i \end{matrix} $$
Explanation
$$ \begin{aligned} x(x+1)(2x+1) &= 12&& \text{simplify left side} \\[1 em](x^2+x)(2x+1) &= 12&& \\[1 em]2x^3+x^2+2x^2+x &= 12&& \\[1 em]2x^3+3x^2+x &= 12&& \text{move all terms to the left hand side } \\[1 em]2x^3+3x^2+x-12 &= 0&& \\[1 em] \end{aligned} $$
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