4c^2+4bc+b^2=0

Solution for 4c^2+4bc+b^2=0 equation:

Simplifying
4c2 + 4bc + b2 = 0

Reorder the terms:
4bc + b2 + 4c2 = 0

Solving
4bc + b2 + 4c2 = 0

Solving for variable 'b'.

Factor a trinomial.
(b + 2c)(b + 2c) = 0

Subproblem 1
Set the factor '(b + 2c)' equal to zero and attempt to solve:

Simplifying
b + 2c = 0

Solving
b + 2c = 0

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

Add '-2c' to each side of the equation.
b + 2c + -2c = 0 + -2c

Combine like terms: 2c + -2c = 0
b + 0 = 0 + -2c
b = 0 + -2c
Remove the zero:
b = -2c

Simplifying
b = -2c
Subproblem 2
Set the factor '(b + 2c)' equal to zero and attempt to solve:

Simplifying
b + 2c = 0

Solving
b + 2c = 0

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

Add '-2c' to each side of the equation.
b + 2c + -2c = 0 + -2c

Combine like terms: 2c + -2c = 0
b + 0 = 0 + -2c
b = 0 + -2c
Remove the zero:
b = -2c

Simplifying
b = -2c
Solution
b = {-2c, -2c}