Решите уравнение: x^3-13x+12=0.

\[x^{3} - 13x + 12\]

\[x^{3} - x - 12x + 12 = 0\]

\[x\left( x^{2} - 1 \right) - 12(x - 1) = 0\]

\[x(x - 1)(x + 1) - 12(x - 1) = 0\]

\[(x - 1)\left( x^{2} + x - 12 \right) = 0\]

\[(x - 1)(x - 3)(x + 4) = 0\]

\[x = 1;\ \ x = 3;\ \ x = - 4.\]