x^3+3x^2+AX+b=0

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

Simplifying
x3 + 3x2 + AX + b = 0

Reorder the terms:
AX + b + 3x2 + x3 = 0

Solving
AX + b + 3x2 + 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 + 3x2 + -1b + x3 = 0 + -1b

Reorder the terms:
AX + b + -1b + 3x2 + x3 = 0 + -1b

Combine like terms: b + -1b = 0
AX + 0 + 3x2 + x3 = 0 + -1b
AX + 3x2 + x3 = 0 + -1b
Remove the zero:
AX + 3x2 + x3 = -1b

Add '-3x2' to each side of the equation.
AX + 3x2 + -3x2 + x3 = -1b + -3x2

Combine like terms: 3x2 + -3x2 = 0
AX + 0 + x3 = -1b + -3x2
AX + x3 = -1b + -3x2

Add '-1x3' to each side of the equation.
AX + x3 + -1x3 = -1b + -3x2 + -1x3

Combine like terms: x3 + -1x3 = 0
AX + 0 = -1b + -3x2 + -1x3
AX = -1b + -3x2 + -1x3

Divide each side by 'X'.
A = -1bX-1 + -3x2X-1 + -1x3X-1

Simplifying
A = -1bX-1 + -3x2X-1 + -1x3X-1