x^3-x^2+ax-b=0

Solution for x^3-x^2+ax-b=0 equation:

Simplifying
x3 + -1x2 + ax + -1b = 0

Reorder the terms:
ax + -1b + -1x2 + x3 = 0

Solving
ax + -1b + -1x2 + x3 = 0

Solving for variable 'a'.

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

Add 'b' to each side of the equation.
ax + -1b + -1x2 + b + x3 = 0 + b

Reorder the terms:
ax + -1b + b + -1x2 + x3 = 0 + b

Combine like terms: -1b + b = 0
ax + 0 + -1x2 + x3 = 0 + b
ax + -1x2 + x3 = 0 + b
Remove the zero:
ax + -1x2 + x3 = b

Add 'x2' to each side of the equation.
ax + -1x2 + x2 + x3 = b + x2

Combine like terms: -1x2 + x2 = 0
ax + 0 + x3 = b + x2
ax + x3 = b + x2

Add '-1x3' to each side of the equation.
ax + x3 + -1x3 = b + x2 + -1x3

Combine like terms: x3 + -1x3 = 0
ax + 0 = b + x2 + -1x3
ax = b + x2 + -1x3

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

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