ab(x+c)+bc(x-a)=ca(b-x)

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Solution for ab(x+c)+bc(x-a)=ca(b-x) equation:


Simplifying
ab(x + c) + bc(x + -1a) = ca(b + -1x)

Reorder the terms:
ab(c + x) + bc(x + -1a) = ca(b + -1x)
(c * ab + x * ab) + bc(x + -1a) = ca(b + -1x)
(abc + abx) + bc(x + -1a) = ca(b + -1x)

Reorder the terms:
abc + abx + bc(-1a + x) = ca(b + -1x)
abc + abx + (-1a * bc + x * bc) = ca(b + -1x)
abc + abx + (-1abc + bcx) = ca(b + -1x)

Reorder the terms:
abc + -1abc + abx + bcx = ca(b + -1x)

Combine like terms: abc + -1abc = 0
0 + abx + bcx = ca(b + -1x)
abx + bcx = ca(b + -1x)
abx + bcx = (b * ac + -1x * ac)
abx + bcx = (abc + -1acx)

Solving
abx + bcx = abc + -1acx

Solving for variable 'a'.

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

Add '-1abc' to each side of the equation.
abx + -1abc + bcx = abc + -1abc + -1acx

Reorder the terms:
-1abc + abx + bcx = abc + -1abc + -1acx

Combine like terms: abc + -1abc = 0
-1abc + abx + bcx = 0 + -1acx
-1abc + abx + bcx = -1acx

Add 'acx' to each side of the equation.
-1abc + abx + acx + bcx = -1acx + acx

Combine like terms: -1acx + acx = 0
-1abc + abx + acx + bcx = 0

Add '-1bcx' to each side of the equation.
-1abc + abx + acx + bcx + -1bcx = 0 + -1bcx

Combine like terms: bcx + -1bcx = 0
-1abc + abx + acx + 0 = 0 + -1bcx
-1abc + abx + acx = 0 + -1bcx
Remove the zero:
-1abc + abx + acx = -1bcx

Combine like terms: -1bcx + bcx = 0
-1abc + abx + acx + bcx = 0

The solution to this equation could not be determined.

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