$$2(x-2)^3+4(x+7)^3 = 0$$
Answer
$$ \begin{matrix}x_1 = -3.01756 & x_2 = -4.49122+7.39756i & x_3 = -4.49122-7.39756i \end{matrix} $$
Explanation
$$ \begin{aligned} 2(x-2)^3+4(x+7)^3 &= 0&& \text{simplify left side} \\[1 em]2(x^3-6x^2+12x-8)+4(x^3+21x^2+147x+343) &= 0&& \\[1 em]2x^3-12x^2+24x-16+4x^3+84x^2+588x+1372 &= 0&& \\[1 em]6x^3+72x^2+612x+1356 &= 0&& \\[1 em] \end{aligned} $$
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