(Ax+b)(Ax+b)=0

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Solution for (Ax+b)(Ax+b)=0 equation: 


Simplifying
(Ax + b)(Ax + b) = 0

Reorder the terms:
(b + xA)(Ax + b) = 0

Reorder the terms:
(b + xA)(b + xA) = 0

Multiply (b + xA) * (b + xA)
(b(b + xA) + xA(b + xA)) = 0
((b * b + xA * b) + xA(b + xA)) = 0

Reorder the terms:
((bxA + b2) + xA(b + xA)) = 0
((bxA + b2) + xA(b + xA)) = 0
(bxA + b2 + (b * xA + xA * xA)) = 0
(bxA + b2 + (bxA + x2A2)) = 0

Reorder the terms:
(bxA + bxA + b2 + x2A2) = 0

Combine like terms: bxA + bxA = 2bxA
(2bxA + b2 + x2A2) = 0

Solving
2bxA + b2 + x2A2 = 0

Solving for variable 'b'.

Factor a trinomial.
(b + xA)(b + xA) = 0


Subproblem 1
Set the factor '(b + xA)' equal to zero and attempt to solve:

Simplifying
b + xA = 0

Solving
b + xA = 0

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

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

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

Simplifying
b = -1xA

Subproblem 2
Set the factor '(b + xA)' equal to zero and attempt to solve:

Simplifying
b + xA = 0

Solving
b + xA = 0

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

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

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

Simplifying
b = -1xA
Solution
b = {-1xA, -1xA}

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