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

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


Simplifying
a(x + b) + x(b + -1a) = ab(2a + -1x)

Reorder the terms:
a(b + x) + x(b + -1a) = ab(2a + -1x)
(b * a + x * a) + x(b + -1a) = ab(2a + -1x)
(ab + ax) + x(b + -1a) = ab(2a + -1x)

Reorder the terms:
ab + ax + x(-1a + b) = ab(2a + -1x)
ab + ax + (-1a * x + b * x) = ab(2a + -1x)
ab + ax + (-1ax + bx) = ab(2a + -1x)

Combine like terms: ax + -1ax = 0
ab + 0 + bx = ab(2a + -1x)
ab + bx = ab(2a + -1x)
ab + bx = (2a * ab + -1x * ab)

Reorder the terms:
ab + bx = (-1abx + 2a2b)
ab + bx = (-1abx + 2a2b)

Solving
ab + bx = -1abx + 2a2b

Solving for variable 'a'.

Reorder the terms:
ab + abx + -2a2b + bx = -1abx + 2a2b + abx + -2a2b

Reorder the terms:
ab + abx + -2a2b + bx = -1abx + abx + 2a2b + -2a2b

Combine like terms: -1abx + abx = 0
ab + abx + -2a2b + bx = 0 + 2a2b + -2a2b
ab + abx + -2a2b + bx = 2a2b + -2a2b

Combine like terms: 2a2b + -2a2b = 0
ab + abx + -2a2b + bx = 0

Factor out the Greatest Common Factor (GCF), 'b'.
b(a + ax + -2a2 + x) = 0


Subproblem 1
Set the factor 'b' equal to zero and attempt to solve:

Simplifying
b = 0

Solving
b = 0

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

Add '-1b' to each side of the equation.
b + -1b = 0 + -1b
Remove the zero:
0 = -1b

Simplifying
0 = -1b

The solution to this equation could not be determined.

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

Subproblem 2
Set the factor '(a + ax + -2a2 + x)' equal to zero and attempt to solve:

Simplifying
a + ax + -2a2 + x = 0

Solving
a + ax + -2a2 + x = 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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