A new method, called Alnahas' method for solving cubic equations, is introduced. This method, similar to Cardano's method, transforms solving a cubic equation into a new question. The question becomes solving equations with multiple variables. This leads to finding one root of the cubic equation. The question then becomes solving a quadratic equation which gives the other two roots.

Solution to a cubic equation

x³ + 6x +7 = 0

Let x = p + q
Then, x³ = p³ + q³ + 3pqx
Or, x³ - 3pqx - (p³ + q³) = 0
Thus, pq = -2         (1)
And, p³ + q³ = -7   (2)
To solve these two equations, we find that:
p = ^-2⁄_q
Substitute p in the second equation, we get:
^-8⁄ ( _q³ ) + q³ = -7
Multiply by q³, we get:
q⁶ + 7q³ -8 = 0
Factor it, considering it as a second degree equation in q³, we find that:
(q³ + 8)(q³ - 1) = 0
Therefore, q = 1, p = -2
and thus, x = -1 is one root of the cubic equation.
Divide the cubic equation by (x+1) we get:
(x + 1)(x² -x +7) = 0
which has the two complex roots:
¹⁄₂ +i ^3√3̅⁄₂ and ¹⁄₂ -i ^3√3̅⁄₂