Simplifying
4AX2 + 4AX + 4A = 0
Reorder the terms:
4A + 4AX + 4AX2 = 0
Solving
4A + 4AX + 4AX2 = 0
Solving for variable 'A'.
Move all terms containing A to the left, all other terms to the right.
Factor out the Greatest Common Factor (GCF), '4A'.
4A(1 + X + X2) = 0
Ignore the factor 4.
Subproblem 1
Set the factor 'A' equal to zero and attempt to solve:
Simplifying
A = 0
Solving
A = 0
Move all terms containing A to the left, all other terms to the right.
Simplifying
A = 0
Subproblem 2
Set the factor '(1 + X + X2)' equal to zero and attempt to solve:
Simplifying
1 + X + X2 = 0
Solving
1 + X + X2 = 0
Move all terms containing A to the left, all other terms to the right.
Add '-1' to each side of the equation.
1 + X + -1 + X2 = 0 + -1
Reorder the terms:
1 + -1 + X + X2 = 0 + -1
Combine like terms: 1 + -1 = 0
0 + X + X2 = 0 + -1
X + X2 = 0 + -1
Combine like terms: 0 + -1 = -1
X + X2 = -1
Add '-1X' to each side of the equation.
X + -1X + X2 = -1 + -1X
Combine like terms: X + -1X = 0
0 + X2 = -1 + -1X
X2 = -1 + -1X
Add '-1X2' to each side of the equation.
X2 + -1X2 = -1 + -1X + -1X2
Combine like terms: X2 + -1X2 = 0
0 = -1 + -1X + -1X2
Simplifying
0 = -1 + -1X + -1X2
The solution to this equation could not be determined.
This subproblem is being ignored because a solution could not be determined.
Solution
A = {0}