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

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


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

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

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

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

Reorder the terms:
4ab + -2ax + -2bx + x2 = -2a2 + -2b2 + x2

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

Combine like terms: x2 + -1x2 = 0
4ab + -2ax + -2bx + 0 = -2a2 + -2b2 + x2 + -1x2
4ab + -2ax + -2bx = -2a2 + -2b2 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
4ab + -2ax + -2bx = -2a2 + -2b2 + 0
4ab + -2ax + -2bx = -2a2 + -2b2

Solving
4ab + -2ax + -2bx = -2a2 + -2b2

Solving for variable 'a'.

Reorder the terms:
4ab + -2ax + 2a2 + -2bx + 2b2 = -2a2 + -2b2 + 2a2 + 2b2

Reorder the terms:
4ab + -2ax + 2a2 + -2bx + 2b2 = -2a2 + 2a2 + -2b2 + 2b2

Combine like terms: -2a2 + 2a2 = 0
4ab + -2ax + 2a2 + -2bx + 2b2 = 0 + -2b2 + 2b2
4ab + -2ax + 2a2 + -2bx + 2b2 = -2b2 + 2b2

Combine like terms: -2b2 + 2b2 = 0
4ab + -2ax + 2a2 + -2bx + 2b2 = 0

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

Ignore the factor 2.

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

Simplifying
2ab + -1ax + a2 + -1bx + b2 = 0

Solving
2ab + -1ax + a2 + -1bx + b2 = 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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