a*b*c+a*c*c+d*b*c=b*c*c

Solution for a*b*c+a*c*c+d*b*c=b*c*c equation:

Simplifying
a * b * c + a * c * c + d * b * c = b * c * c

Multiply a * b
ab * c + a * c * c + d * b * c = b * c * c

Multiply ab * c
abc + a * c * c + d * b * c = b * c * c

Multiply a * c
abc + ac * c + d * b * c = b * c * c

Multiply ac * c
abc + ac2 + d * b * c = b * c * c

Multiply d * b
abc + ac2 + bd * c = b * c * c

Multiply bd * c
abc + ac2 + bcd = b * c * c

Multiply b * c
abc + ac2 + bcd = bc * c

Multiply bc * c
abc + ac2 + bcd = bc2

Solving
abc + ac2 + bcd = bc2

Solving for variable 'a'.

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

Add '-1bcd' to each side of the equation.
abc + ac2 + bcd + -1bcd = -1bcd + bc2

Combine like terms: bcd + -1bcd = 0
abc + ac2 + 0 = -1bcd + bc2
abc + ac2 = -1bcd + bc2

Reorder the terms:
abc + ac2 + bcd + -1bc2 = -1bcd + bcd + bc2 + -1bc2

Combine like terms: -1bcd + bcd = 0
abc + ac2 + bcd + -1bc2 = 0 + bc2 + -1bc2
abc + ac2 + bcd + -1bc2 = bc2 + -1bc2

Combine like terms: bc2 + -1bc2 = 0
abc + ac2 + bcd + -1bc2 = 0

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

Subproblem 1
Set the factor 'c' equal to zero and attempt to solve:

Simplifying
c = 0

Solving
c = 0

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

Add '-1c' to each side of the equation.
c + -1c = 0 + -1c
Remove the zero:
0 = -1c

Simplifying
0 = -1c

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(ab + ac + bd + -1bc)' equal to zero and attempt to solve:

Simplifying
ab + ac + bd + -1bc = 0

Reorder the terms:
ab + ac + -1bc + bd = 0

Solving
ab + ac + -1bc + bd = 0

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

Add 'bc' to each side of the equation.
ab + ac + -1bc + bc + bd = 0 + bc

Combine like terms: -1bc + bc = 0
ab + ac + 0 + bd = 0 + bc
ab + ac + bd = 0 + bc
Remove the zero:
ab + ac + bd = bc

Add '-1bd' to each side of the equation.
ab + ac + bd + -1bd = bc + -1bd

Combine like terms: bd + -1bd = 0
ab + ac + 0 = bc + -1bd
ab + ac = bc + -1bd

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.