x^2+2x=A(x^2-2)+(Bx+C)(2x-4)

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Solution for x^2+2x=A(x^2-2)+(Bx+C)(2x-4) equation: 


Simplifying
x2 + 2x = A(x2 + -2) + (Bx + C)(2x + -4)

Reorder the terms:
2x + x2 = A(x2 + -2) + (Bx + C)(2x + -4)

Reorder the terms:
2x + x2 = A(-2 + x2) + (Bx + C)(2x + -4)
2x + x2 = (-2 * A + x2 * A) + (Bx + C)(2x + -4)
2x + x2 = (-2A + x2A) + (Bx + C)(2x + -4)

Reorder the terms:
2x + x2 = -2A + x2A + (C + xB)(2x + -4)

Reorder the terms:
2x + x2 = -2A + x2A + (C + xB)(-4 + 2x)

Multiply (C + xB) * (-4 + 2x)
2x + x2 = -2A + x2A + (C(-4 + 2x) + xB(-4 + 2x))
2x + x2 = -2A + x2A + ((-4 * C + 2x * C) + xB(-4 + 2x))
2x + x2 = -2A + x2A + ((-4C + 2xC) + xB(-4 + 2x))
2x + x2 = -2A + x2A + (-4C + 2xC + (-4 * xB + 2x * xB))
2x + x2 = -2A + x2A + (-4C + 2xC + (-4xB + 2x2B))

Reorder the terms:
2x + x2 = -2A + x2A + (-4C + -4xB + 2xC + 2x2B)
2x + x2 = -2A + x2A + (-4C + -4xB + 2xC + 2x2B)

Reorder the terms:
2x + x2 = -2A + -4C + -4xB + 2xC + x2A + 2x2B

Solving
2x + x2 = -2A + -4C + -4xB + 2xC + x2A + 2x2B

Solving for variable 'x'.

Reorder the terms:
2A + 4C + 2x + 4xB + -2xC + x2 + -1x2A + -2x2B = -2A + -4C + -4xB + 2xC + x2A + 2x2B + 2A + 4C + 4xB + -2xC + -1x2A + -2x2B

Reorder the terms:
2A + 4C + 2x + 4xB + -2xC + x2 + -1x2A + -2x2B = -2A + 2A + -4C + 4C + -4xB + 4xB + 2xC + -2xC + x2A + -1x2A + 2x2B + -2x2B

Combine like terms: -2A + 2A = 0
2A + 4C + 2x + 4xB + -2xC + x2 + -1x2A + -2x2B = 0 + -4C + 4C + -4xB + 4xB + 2xC + -2xC + x2A + -1x2A + 2x2B + -2x2B
2A + 4C + 2x + 4xB + -2xC + x2 + -1x2A + -2x2B = -4C + 4C + -4xB + 4xB + 2xC + -2xC + x2A + -1x2A + 2x2B + -2x2B

Combine like terms: -4C + 4C = 0
2A + 4C + 2x + 4xB + -2xC + x2 + -1x2A + -2x2B = 0 + -4xB + 4xB + 2xC + -2xC + x2A + -1x2A + 2x2B + -2x2B
2A + 4C + 2x + 4xB + -2xC + x2 + -1x2A + -2x2B = -4xB + 4xB + 2xC + -2xC + x2A + -1x2A + 2x2B + -2x2B

Combine like terms: -4xB + 4xB = 0
2A + 4C + 2x + 4xB + -2xC + x2 + -1x2A + -2x2B = 0 + 2xC + -2xC + x2A + -1x2A + 2x2B + -2x2B
2A + 4C + 2x + 4xB + -2xC + x2 + -1x2A + -2x2B = 2xC + -2xC + x2A + -1x2A + 2x2B + -2x2B

Combine like terms: 2xC + -2xC = 0
2A + 4C + 2x + 4xB + -2xC + x2 + -1x2A + -2x2B = 0 + x2A + -1x2A + 2x2B + -2x2B
2A + 4C + 2x + 4xB + -2xC + x2 + -1x2A + -2x2B = x2A + -1x2A + 2x2B + -2x2B

Combine like terms: x2A + -1x2A = 0
2A + 4C + 2x + 4xB + -2xC + x2 + -1x2A + -2x2B = 0 + 2x2B + -2x2B
2A + 4C + 2x + 4xB + -2xC + x2 + -1x2A + -2x2B = 2x2B + -2x2B

Combine like terms: 2x2B + -2x2B = 0
2A + 4C + 2x + 4xB + -2xC + x2 + -1x2A + -2x2B = 0

The solution to this equation could not be determined.

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