(x-2)(x-2b)=x^2-2(a^2+b^2)

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Solution for (x-2)(x-2b)=x^2-2(a^2+b^2) equation: 


Simplifying
(x + -2)(x + -2b) = x2 + -2(a2 + b2)

Reorder the terms:
(-2 + x)(x + -2b) = x2 + -2(a2 + b2)

Reorder the terms:
(-2 + x)(-2b + x) = x2 + -2(a2 + b2)

Multiply (-2 + x) * (-2b + x)
(-2(-2b + x) + x(-2b + x)) = x2 + -2(a2 + b2)
((-2b * -2 + x * -2) + x(-2b + x)) = x2 + -2(a2 + b2)
((4b + -2x) + x(-2b + x)) = x2 + -2(a2 + b2)
(4b + -2x + (-2b * x + x * x)) = x2 + -2(a2 + b2)
(4b + -2x + (-2bx + x2)) = x2 + -2(a2 + b2)

Reorder the terms:
(4b + -2bx + -2x + x2) = x2 + -2(a2 + b2)
(4b + -2bx + -2x + x2) = x2 + -2(a2 + b2)
4b + -2bx + -2x + x2 = x2 + (a2 * -2 + b2 * -2)
4b + -2bx + -2x + x2 = x2 + (-2a2 + -2b2)

Reorder the terms:
4b + -2bx + -2x + x2 = -2a2 + -2b2 + x2

Add '-1x2' to each side of the equation.
4b + -2bx + -2x + x2 + -1x2 = -2a2 + -2b2 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
4b + -2bx + -2x + 0 = -2a2 + -2b2 + x2 + -1x2
4b + -2bx + -2x = -2a2 + -2b2 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
4b + -2bx + -2x = -2a2 + -2b2 + 0
4b + -2bx + -2x = -2a2 + -2b2

Solving
4b + -2bx + -2x = -2a2 + -2b2

Solving for variable 'b'.

Reorder the terms:
2a2 + 4b + -2bx + 2b2 + -2x = -2a2 + -2b2 + 2a2 + 2b2

Reorder the terms:
2a2 + 4b + -2bx + 2b2 + -2x = -2a2 + 2a2 + -2b2 + 2b2

Combine like terms: -2a2 + 2a2 = 0
2a2 + 4b + -2bx + 2b2 + -2x = 0 + -2b2 + 2b2
2a2 + 4b + -2bx + 2b2 + -2x = -2b2 + 2b2

Combine like terms: -2b2 + 2b2 = 0
2a2 + 4b + -2bx + 2b2 + -2x = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(a2 + 2b + -1bx + b2 + -1x) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(a2 + 2b + -1bx + b2 + -1x)' equal to zero and attempt to solve:

Simplifying
a2 + 2b + -1bx + b2 + -1x = 0

Solving
a2 + 2b + -1bx + b2 + -1x = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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