A*B+(1-A)*(C*D-(1-C)*E)=F

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Solution for A*B+(1-A)*(C*D-(1-C)*E)=F equation: 


Simplifying
A * B + (1 + -1A)(C * D + -1(1 + -1C) * E) = F

Multiply A * B
AB + (1 + -1A)(C * D + -1(1 + -1C) * E) = F

Multiply C * D
AB + (1 + -1A)(CD + -1(1 + -1C) * E) = F

Reorder the terms for easier multiplication:
AB + (1 + -1A)(CD + -1E(1 + -1C)) = F
AB + (1 + -1A)(CD + (1 * -1E + -1C * -1E)) = F

Reorder the terms:
AB + (1 + -1A)(CD + (1CE + -1E)) = F
AB + (1 + -1A)(CD + (1CE + -1E)) = F

Multiply (1 + -1A) * (CD + 1CE + -1E)
AB + (1(CD + 1CE + -1E) + -1A * (CD + 1CE + -1E)) = F
AB + ((CD * 1 + 1CE * 1 + -1E * 1) + -1A * (CD + 1CE + -1E)) = F
AB + ((1CD + 1CE + -1E) + -1A * (CD + 1CE + -1E)) = F
AB + (1CD + 1CE + -1E + (CD * -1A + 1CE * -1A + -1E * -1A)) = F
AB + (1CD + 1CE + -1E + (-1ACD + -1ACE + 1AE)) = F

Reorder the terms:
AB + (-1ACD + -1ACE + 1AE + 1CD + 1CE + -1E) = F
AB + (-1ACD + -1ACE + 1AE + 1CD + 1CE + -1E) = F

Solving
AB + -1ACD + -1ACE + 1AE + 1CD + 1CE + -1E = F

Solving for variable 'A'.

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

Add '-1CD' to each side of the equation.
AB + -1ACD + -1ACE + 1AE + 1CD + 1CE + -1CD + -1E = -1CD + F

Reorder the terms:
AB + -1ACD + -1ACE + 1AE + 1CD + -1CD + 1CE + -1E = -1CD + F

Combine like terms: 1CD + -1CD = 0
AB + -1ACD + -1ACE + 1AE + 0 + 1CE + -1E = -1CD + F
AB + -1ACD + -1ACE + 1AE + 1CE + -1E = -1CD + F

Add '-1CE' to each side of the equation.
AB + -1ACD + -1ACE + 1AE + 1CE + -1CE + -1E = -1CD + -1CE + F

Combine like terms: 1CE + -1CE = 0
AB + -1ACD + -1ACE + 1AE + 0 + -1E = -1CD + -1CE + F
AB + -1ACD + -1ACE + 1AE + -1E = -1CD + -1CE + F

Add 'E' to each side of the equation.
AB + -1ACD + -1ACE + 1AE + -1E + E = -1CD + -1CE + E + F

Combine like terms: -1E + E = 0
AB + -1ACD + -1ACE + 1AE + 0 = -1CD + -1CE + E + F
AB + -1ACD + -1ACE + 1AE = -1CD + -1CE + E + F

Reorder the terms:
AB + -1ACD + -1ACE + 1AE + CD + CE + -1E + -1F = -1CD + CD + -1CE + CE + E + -1E + F + -1F

Combine like terms: -1CD + CD = 0
AB + -1ACD + -1ACE + 1AE + CD + CE + -1E + -1F = 0 + -1CE + CE + E + -1E + F + -1F
AB + -1ACD + -1ACE + 1AE + CD + CE + -1E + -1F = -1CE + CE + E + -1E + F + -1F

Combine like terms: -1CE + CE = 0
AB + -1ACD + -1ACE + 1AE + CD + CE + -1E + -1F = 0 + E + -1E + F + -1F
AB + -1ACD + -1ACE + 1AE + CD + CE + -1E + -1F = E + -1E + F + -1F

Combine like terms: E + -1E = 0
AB + -1ACD + -1ACE + 1AE + CD + CE + -1E + -1F = 0 + F + -1F
AB + -1ACD + -1ACE + 1AE + CD + CE + -1E + -1F = F + -1F

Combine like terms: F + -1F = 0
AB + -1ACD + -1ACE + 1AE + CD + CE + -1E + -1F = 0

The solution to this equation could not be determined.

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