Ax(x-1)+B(x+1)(x-1)+C(x+1)x=x^2+4

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Solution for Ax(x-1)+B(x+1)(x-1)+C(x+1)x=x^2+4 equation: 


Simplifying
Ax(x + -1) + B(x + 1)(x + -1) + C(x + 1) * x = x2 + 4

Reorder the terms:
xA(-1 + x) + B(x + 1)(x + -1) + C(x + 1) * x = x2 + 4
(-1 * xA + x * xA) + B(x + 1)(x + -1) + C(x + 1) * x = x2 + 4
(-1xA + x2A) + B(x + 1)(x + -1) + C(x + 1) * x = x2 + 4

Reorder the terms:
-1xA + x2A + B(1 + x)(x + -1) + C(x + 1) * x = x2 + 4

Reorder the terms:
-1xA + x2A + B(1 + x)(-1 + x) + C(x + 1) * x = x2 + 4

Multiply (1 + x) * (-1 + x)
-1xA + x2A + B(1(-1 + x) + x(-1 + x)) + C(x + 1) * x = x2 + 4
-1xA + x2A + B((-1 * 1 + x * 1) + x(-1 + x)) + C(x + 1) * x = x2 + 4
-1xA + x2A + B((-1 + 1x) + x(-1 + x)) + C(x + 1) * x = x2 + 4
-1xA + x2A + B(-1 + 1x + (-1 * x + x * x)) + C(x + 1) * x = x2 + 4
-1xA + x2A + B(-1 + 1x + (-1x + x2)) + C(x + 1) * x = x2 + 4

Combine like terms: 1x + -1x = 0
-1xA + x2A + B(-1 + 0 + x2) + C(x + 1) * x = x2 + 4
-1xA + x2A + B(-1 + x2) + C(x + 1) * x = x2 + 4
-1xA + x2A + (-1 * B + x2 * B) + C(x + 1) * x = x2 + 4
-1xA + x2A + (-1B + x2B) + C(x + 1) * x = x2 + 4

Reorder the terms:
-1xA + x2A + -1B + x2B + C(1 + x) * x = x2 + 4

Reorder the terms for easier multiplication:
-1xA + x2A + -1B + x2B + C * x(1 + x) = x2 + 4

Multiply C * x
-1xA + x2A + -1B + x2B + xC(1 + x) = x2 + 4
-1xA + x2A + -1B + x2B + (1 * xC + x * xC) = x2 + 4
-1xA + x2A + -1B + x2B + (1xC + x2C) = x2 + 4

Reorder the terms:
-1B + -1xA + 1xC + x2A + x2B + x2C = x2 + 4

Reorder the terms:
-1B + -1xA + 1xC + x2A + x2B + x2C = 4 + x2

Solving
-1B + -1xA + 1xC + x2A + x2B + x2C = 4 + x2

Solving for variable 'B'.

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

Add 'xA' to each side of the equation.
-1B + -1xA + 1xC + x2A + x2B + xA + x2C = 4 + xA + x2

Reorder the terms:
-1B + -1xA + xA + 1xC + x2A + x2B + x2C = 4 + xA + x2

Combine like terms: -1xA + xA = 0
-1B + 0 + 1xC + x2A + x2B + x2C = 4 + xA + x2
-1B + 1xC + x2A + x2B + x2C = 4 + xA + x2

Add '-1xC' to each side of the equation.
-1B + 1xC + x2A + x2B + -1xC + x2C = 4 + xA + -1xC + x2

Reorder the terms:
-1B + 1xC + -1xC + x2A + x2B + x2C = 4 + xA + -1xC + x2

Combine like terms: 1xC + -1xC = 0
-1B + 0 + x2A + x2B + x2C = 4 + xA + -1xC + x2
-1B + x2A + x2B + x2C = 4 + xA + -1xC + x2

Add '-1x2A' to each side of the equation.
-1B + x2A + x2B + -1x2A + x2C = 4 + xA + -1xC + x2 + -1x2A

Reorder the terms:
-1B + x2A + -1x2A + x2B + x2C = 4 + xA + -1xC + x2 + -1x2A

Combine like terms: x2A + -1x2A = 0
-1B + 0 + x2B + x2C = 4 + xA + -1xC + x2 + -1x2A
-1B + x2B + x2C = 4 + xA + -1xC + x2 + -1x2A

Add '-1x2C' to each side of the equation.
-1B + x2B + x2C + -1x2C = 4 + xA + -1xC + x2 + -1x2A + -1x2C

Combine like terms: x2C + -1x2C = 0
-1B + x2B + 0 = 4 + xA + -1xC + x2 + -1x2A + -1x2C
-1B + x2B = 4 + xA + -1xC + x2 + -1x2A + -1x2C

Reorder the terms:
-4 + -1B + -1xA + xC + -1x2 + x2A + x2B + x2C = 4 + xA + -1xC + x2 + -1x2A + -1x2C + -4 + -1xA + xC + -1x2 + x2A + x2C

Reorder the terms:
-4 + -1B + -1xA + xC + -1x2 + x2A + x2B + x2C = 4 + -4 + xA + -1xA + -1xC + xC + x2 + -1x2 + -1x2A + x2A + -1x2C + x2C

Combine like terms: 4 + -4 = 0
-4 + -1B + -1xA + xC + -1x2 + x2A + x2B + x2C = 0 + xA + -1xA + -1xC + xC + x2 + -1x2 + -1x2A + x2A + -1x2C + x2C
-4 + -1B + -1xA + xC + -1x2 + x2A + x2B + x2C = xA + -1xA + -1xC + xC + x2 + -1x2 + -1x2A + x2A + -1x2C + x2C

Combine like terms: xA + -1xA = 0
-4 + -1B + -1xA + xC + -1x2 + x2A + x2B + x2C = 0 + -1xC + xC + x2 + -1x2 + -1x2A + x2A + -1x2C + x2C
-4 + -1B + -1xA + xC + -1x2 + x2A + x2B + x2C = -1xC + xC + x2 + -1x2 + -1x2A + x2A + -1x2C + x2C

Combine like terms: -1xC + xC = 0
-4 + -1B + -1xA + xC + -1x2 + x2A + x2B + x2C = 0 + x2 + -1x2 + -1x2A + x2A + -1x2C + x2C
-4 + -1B + -1xA + xC + -1x2 + x2A + x2B + x2C = x2 + -1x2 + -1x2A + x2A + -1x2C + x2C

Combine like terms: x2 + -1x2 = 0
-4 + -1B + -1xA + xC + -1x2 + x2A + x2B + x2C = 0 + -1x2A + x2A + -1x2C + x2C
-4 + -1B + -1xA + xC + -1x2 + x2A + x2B + x2C = -1x2A + x2A + -1x2C + x2C

Combine like terms: -1x2A + x2A = 0
-4 + -1B + -1xA + xC + -1x2 + x2A + x2B + x2C = 0 + -1x2C + x2C
-4 + -1B + -1xA + xC + -1x2 + x2A + x2B + x2C = -1x2C + x2C

Combine like terms: -1x2C + x2C = 0
-4 + -1B + -1xA + xC + -1x2 + x2A + x2B + x2C = 0

The solution to this equation could not be determined.

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