(ab+bc)(ab+bc)=

Solution for (ab+bc)(ab+bc)= equation:

Simplifying
(ab + bc)(ab + bc) = 0

Multiply (ab + bc) * (ab + bc)
(ab(ab + bc) + bc(ab + bc)) = 0
((ab * ab + bc * ab) + bc(ab + bc)) = 0

Reorder the terms:
((ab2c + a2b2) + bc(ab + bc)) = 0
((ab2c + a2b2) + bc(ab + bc)) = 0
(ab2c + a2b2 + (ab * bc + bc * bc)) = 0
(ab2c + a2b2 + (ab2c + b2c2)) = 0

Reorder the terms:
(ab2c + ab2c + a2b2 + b2c2) = 0

Combine like terms: ab2c + ab2c = 2ab2c
(2ab2c + a2b2 + b2c2) = 0

Solving
2ab2c + a2b2 + b2c2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'b2'.
b2(2ac + a2 + c2) = 0

Factor a trinomial.
b2((a + c)(a + c)) = 0

Subproblem 1
Set the factor 'b2' equal to zero and attempt to solve:

Simplifying
b2 = 0

Solving
b2 = 0

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

Add '-1b2' to each side of the equation.
b2 + -1b2 = 0 + -1b2
Remove the zero:
0 = -1b2

Simplifying
0 = -1b2

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 '(a + c)' equal to zero and attempt to solve:

Simplifying
a + c = 0

Solving
a + c = 0

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

Add '-1c' to each side of the equation.
a + c + -1c = 0 + -1c

Combine like terms: c + -1c = 0
a + 0 = 0 + -1c
a = 0 + -1c
Remove the zero:
a = -1c

Simplifying
a = -1c
Subproblem 3
Set the factor '(a + c)' equal to zero and attempt to solve:

Simplifying
a + c = 0

Solving
a + c = 0

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

Add '-1c' to each side of the equation.
a + c + -1c = 0 + -1c

Combine like terms: c + -1c = 0
a + 0 = 0 + -1c
a = 0 + -1c
Remove the zero:
a = -1c

Simplifying
a = -1c
Solution
a = {-1c, -1c}