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

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


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

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

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

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

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

Reorder the terms:
ax + bx = (-1ax + a2) + b(b + -1x)
ax + bx = (-1ax + a2) + b(b + -1x)
ax + bx = -1ax + a2 + (b * b + -1x * b)

Reorder the terms:
ax + bx = -1ax + a2 + (-1bx + b2)
ax + bx = -1ax + a2 + (-1bx + b2)

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

Solving for variable 'a'.

Reorder the terms:
ax + ax + -1a2 + bx + bx + -1b2 = -1ax + a2 + -1bx + b2 + ax + -1a2 + bx + -1b2

Combine like terms: ax + ax = 2ax
2ax + -1a2 + bx + bx + -1b2 = -1ax + a2 + -1bx + b2 + ax + -1a2 + bx + -1b2

Combine like terms: bx + bx = 2bx
2ax + -1a2 + 2bx + -1b2 = -1ax + a2 + -1bx + b2 + ax + -1a2 + bx + -1b2

Reorder the terms:
2ax + -1a2 + 2bx + -1b2 = -1ax + ax + a2 + -1a2 + -1bx + bx + b2 + -1b2

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

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

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

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

The solution to this equation could not be determined.

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