x^3+ax+b=0

Solution for x^3+ax+b=0 equation:

Simplifying
x3 + ax + b = 0

Reorder the terms:
ax + b + x3 = 0

Solving
ax + b + x3 = 0

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-1b' to each side of the equation.
ax + b + -1b + x3 = 0 + -1b

Combine like terms: b + -1b = 0
ax + 0 + x3 = 0 + -1b
ax + x3 = 0 + -1b
Remove the zero:
ax + x3 = -1b

Add '-1x3' to each side of the equation.
ax + x3 + -1x3 = -1b + -1x3

Combine like terms: x3 + -1x3 = 0
ax + 0 = -1b + -1x3
ax = -1b + -1x3

Divide each side by 'x'.
a = -1bx-1 + -1x2

Simplifying
a = -1bx-1 + -1x2