(Y-3)(Y^2+BY+C)=Y^3-27

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Solution for (Y-3)(Y^2+BY+C)=Y^3-27 equation: 


Simplifying
(Y + -3)(Y2 + BY + C) = Y3 + -27

Reorder the terms:
(-3 + Y)(Y2 + BY + C) = Y3 + -27

Reorder the terms:
(-3 + Y)(BY + C + Y2) = Y3 + -27

Multiply (-3 + Y) * (BY + C + Y2)
(-3(BY + C + Y2) + Y(BY + C + Y2)) = Y3 + -27
((BY * -3 + C * -3 + Y2 * -3) + Y(BY + C + Y2)) = Y3 + -27
((-3BY + -3C + -3Y2) + Y(BY + C + Y2)) = Y3 + -27
(-3BY + -3C + -3Y2 + (BY * Y + C * Y + Y2 * Y)) = Y3 + -27
(-3BY + -3C + -3Y2 + (BY2 + CY + Y3)) = Y3 + -27

Reorder the terms:
(-3BY + BY2 + -3C + CY + -3Y2 + Y3) = Y3 + -27
(-3BY + BY2 + -3C + CY + -3Y2 + Y3) = Y3 + -27

Reorder the terms:
-3BY + BY2 + -3C + CY + -3Y2 + Y3 = -27 + Y3

Add '-1Y3' to each side of the equation.
-3BY + BY2 + -3C + CY + -3Y2 + Y3 + -1Y3 = -27 + Y3 + -1Y3

Combine like terms: Y3 + -1Y3 = 0
-3BY + BY2 + -3C + CY + -3Y2 + 0 = -27 + Y3 + -1Y3
-3BY + BY2 + -3C + CY + -3Y2 = -27 + Y3 + -1Y3

Combine like terms: Y3 + -1Y3 = 0
-3BY + BY2 + -3C + CY + -3Y2 = -27 + 0
-3BY + BY2 + -3C + CY + -3Y2 = -27

Solving
-3BY + BY2 + -3C + CY + -3Y2 = -27

Solving for variable 'B'.

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

Add '3C' to each side of the equation.
-3BY + BY2 + -3C + CY + 3C + -3Y2 = -27 + 3C

Reorder the terms:
-3BY + BY2 + -3C + 3C + CY + -3Y2 = -27 + 3C

Combine like terms: -3C + 3C = 0
-3BY + BY2 + 0 + CY + -3Y2 = -27 + 3C
-3BY + BY2 + CY + -3Y2 = -27 + 3C

Add '-1CY' to each side of the equation.
-3BY + BY2 + CY + -1CY + -3Y2 = -27 + 3C + -1CY

Combine like terms: CY + -1CY = 0
-3BY + BY2 + 0 + -3Y2 = -27 + 3C + -1CY
-3BY + BY2 + -3Y2 = -27 + 3C + -1CY

Add '3Y2' to each side of the equation.
-3BY + BY2 + -3Y2 + 3Y2 = -27 + 3C + -1CY + 3Y2

Combine like terms: -3Y2 + 3Y2 = 0
-3BY + BY2 + 0 = -27 + 3C + -1CY + 3Y2
-3BY + BY2 = -27 + 3C + -1CY + 3Y2

Reorder the terms:
27 + -3BY + BY2 + -3C + CY + -3Y2 = -27 + 3C + -1CY + 3Y2 + 27 + -3C + CY + -3Y2

Reorder the terms:
27 + -3BY + BY2 + -3C + CY + -3Y2 = -27 + 27 + 3C + -3C + -1CY + CY + 3Y2 + -3Y2

Combine like terms: -27 + 27 = 0
27 + -3BY + BY2 + -3C + CY + -3Y2 = 0 + 3C + -3C + -1CY + CY + 3Y2 + -3Y2
27 + -3BY + BY2 + -3C + CY + -3Y2 = 3C + -3C + -1CY + CY + 3Y2 + -3Y2

Combine like terms: 3C + -3C = 0
27 + -3BY + BY2 + -3C + CY + -3Y2 = 0 + -1CY + CY + 3Y2 + -3Y2
27 + -3BY + BY2 + -3C + CY + -3Y2 = -1CY + CY + 3Y2 + -3Y2

Combine like terms: -1CY + CY = 0
27 + -3BY + BY2 + -3C + CY + -3Y2 = 0 + 3Y2 + -3Y2
27 + -3BY + BY2 + -3C + CY + -3Y2 = 3Y2 + -3Y2

Combine like terms: 3Y2 + -3Y2 = 0
27 + -3BY + BY2 + -3C + CY + -3Y2 = 0

The solution to this equation could not be determined.

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