=(1+a)(1+b)(1+c)

Solution for =(1+a)(1+b)(1+c) equation:

Simplifying
0 = (1 + a)(1 + b)(1 + c)

Multiply (1 + a) * (1 + b)
0 = (1(1 + b) + a(1 + b))(1 + c)
0 = ((1 * 1 + b * 1) + a(1 + b))(1 + c)
0 = ((1 + 1b) + a(1 + b))(1 + c)
0 = (1 + 1b + (1 * a + b * a))(1 + c)
0 = (1 + 1b + (1a + ab))(1 + c)

Reorder the terms:
0 = (1 + 1a + ab + 1b)(1 + c)
0 = (1 + 1a + ab + 1b)(1 + c)

Multiply (1 + 1a + ab + 1b) * (1 + c)
0 = (1(1 + c) + 1a * (1 + c) + ab(1 + c) + 1b * (1 + c))
0 = ((1 * 1 + c * 1) + 1a * (1 + c) + ab(1 + c) + 1b * (1 + c))
0 = ((1 + 1c) + 1a * (1 + c) + ab(1 + c) + 1b * (1 + c))
0 = (1 + 1c + (1 * 1a + c * 1a) + ab(1 + c) + 1b * (1 + c))
0 = (1 + 1c + (1a + 1ac) + ab(1 + c) + 1b * (1 + c))
0 = (1 + 1c + 1a + 1ac + (1 * ab + c * ab) + 1b * (1 + c))
0 = (1 + 1c + 1a + 1ac + (1ab + abc) + 1b * (1 + c))
0 = (1 + 1c + 1a + 1ac + 1ab + abc + (1 * 1b + c * 1b))
0 = (1 + 1c + 1a + 1ac + 1ab + abc + (1b + 1bc))

Reorder the terms:
0 = (1 + 1a + 1ab + abc + 1ac + 1b + 1bc + 1c)
0 = (1 + 1a + 1ab + abc + 1ac + 1b + 1bc + 1c)

Solving
0 = 1 + 1a + 1ab + abc + 1ac + 1b + 1bc + 1c

Solving for variable 'a'.

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

Add '-1a' to each side of the equation.
0 + -1a = 1 + 1a + 1ab + abc + 1ac + 1b + 1bc + -1a + 1c
Remove the zero:
-1a = 1 + 1a + 1ab + abc + 1ac + 1b + 1bc + -1a + 1c

Reorder the terms:
-1a = 1 + 1a + -1a + 1ab + abc + 1ac + 1b + 1bc + 1c

Combine like terms: 1a + -1a = 0
-1a = 1 + 0 + 1ab + abc + 1ac + 1b + 1bc + 1c
-1a = 1 + 1ab + abc + 1ac + 1b + 1bc + 1c

Add '-1ab' to each side of the equation.
-1a + -1ab = 1 + 1ab + abc + 1ac + 1b + 1bc + -1ab + 1c

Reorder the terms:
-1a + -1ab = 1 + 1ab + -1ab + abc + 1ac + 1b + 1bc + 1c

Combine like terms: 1ab + -1ab = 0
-1a + -1ab = 1 + 0 + abc + 1ac + 1b + 1bc + 1c
-1a + -1ab = 1 + abc + 1ac + 1b + 1bc + 1c

Add '-1abc' to each side of the equation.
-1a + -1ab + -1abc = 1 + abc + 1ac + 1b + 1bc + -1abc + 1c

Reorder the terms:
-1a + -1ab + -1abc = 1 + abc + -1abc + 1ac + 1b + 1bc + 1c

Combine like terms: abc + -1abc = 0
-1a + -1ab + -1abc = 1 + 0 + 1ac + 1b + 1bc + 1c
-1a + -1ab + -1abc = 1 + 1ac + 1b + 1bc + 1c

Add '-1ac' to each side of the equation.
-1a + -1ab + -1abc + -1ac = 1 + 1ac + 1b + 1bc + -1ac + 1c

Reorder the terms:
-1a + -1ab + -1abc + -1ac = 1 + 1ac + -1ac + 1b + 1bc + 1c

Combine like terms: 1ac + -1ac = 0
-1a + -1ab + -1abc + -1ac = 1 + 0 + 1b + 1bc + 1c
-1a + -1ab + -1abc + -1ac = 1 + 1b + 1bc + 1c

Reorder the terms:
-1 + -1a + -1ab + -1abc + -1ac + -1b + -1bc + -1c = 1 + 1b + 1bc + 1c + -1 + -1b + -1bc + -1c

Reorder the terms:
-1 + -1a + -1ab + -1abc + -1ac + -1b + -1bc + -1c = 1 + -1 + 1b + -1b + 1bc + -1bc + 1c + -1c

Combine like terms: 1 + -1 = 0
-1 + -1a + -1ab + -1abc + -1ac + -1b + -1bc + -1c = 0 + 1b + -1b + 1bc + -1bc + 1c + -1c
-1 + -1a + -1ab + -1abc + -1ac + -1b + -1bc + -1c = 1b + -1b + 1bc + -1bc + 1c + -1c

Combine like terms: 1b + -1b = 0
-1 + -1a + -1ab + -1abc + -1ac + -1b + -1bc + -1c = 0 + 1bc + -1bc + 1c + -1c
-1 + -1a + -1ab + -1abc + -1ac + -1b + -1bc + -1c = 1bc + -1bc + 1c + -1c

Combine like terms: 1bc + -1bc = 0
-1 + -1a + -1ab + -1abc + -1ac + -1b + -1bc + -1c = 0 + 1c + -1c
-1 + -1a + -1ab + -1abc + -1ac + -1b + -1bc + -1c = 1c + -1c

Combine like terms: 1c + -1c = 0
-1 + -1a + -1ab + -1abc + -1ac + -1b + -1bc + -1c = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + a + ab + abc + ac + b + bc + c) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(1 + a + ab + abc + ac + b + bc + c)' equal to zero and attempt to solve:

Simplifying
1 + a + ab + abc + ac + b + bc + c = 0

Solving
1 + a + ab + abc + ac + b + bc + c = 0

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

Add '-1' to each side of the equation.
1 + a + ab + abc + ac + b + bc + -1 + c = 0 + -1

Reorder the terms:
1 + -1 + a + ab + abc + ac + b + bc + c = 0 + -1

Combine like terms: 1 + -1 = 0
0 + a + ab + abc + ac + b + bc + c = 0 + -1
a + ab + abc + ac + b + bc + c = 0 + -1

Combine like terms: 0 + -1 = -1
a + ab + abc + ac + b + bc + c = -1

Add '-1b' to each side of the equation.
a + ab + abc + ac + b + bc + -1b + c = -1 + -1b

Reorder the terms:
a + ab + abc + ac + b + -1b + bc + c = -1 + -1b

Combine like terms: b + -1b = 0
a + ab + abc + ac + 0 + bc + c = -1 + -1b
a + ab + abc + ac + bc + c = -1 + -1b

Add '-1bc' to each side of the equation.
a + ab + abc + ac + bc + -1bc + c = -1 + -1b + -1bc

Combine like terms: bc + -1bc = 0
a + ab + abc + ac + 0 + c = -1 + -1b + -1bc
a + ab + abc + ac + c = -1 + -1b + -1bc

Add '-1c' to each side of the equation.
a + ab + abc + ac + c + -1c = -1 + -1b + -1bc + -1c

Combine like terms: c + -1c = 0
a + ab + abc + ac + 0 = -1 + -1b + -1bc + -1c
a + ab + abc + ac = -1 + -1b + -1bc + -1c

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.