(2b+c)(3b+2c)=0

Solution for (2b+c)(3b+2c)=0 equation:

Simplifying
(2b + c)(3b + 2c) = 0

Multiply (2b + c) * (3b + 2c)
(2b * (3b + 2c) + c(3b + 2c)) = 0
((3b * 2b + 2c * 2b) + c(3b + 2c)) = 0

Reorder the terms:
((4bc + 6b2) + c(3b + 2c)) = 0
((4bc + 6b2) + c(3b + 2c)) = 0
(4bc + 6b2 + (3b * c + 2c * c)) = 0
(4bc + 6b2 + (3bc + 2c2)) = 0

Reorder the terms:
(4bc + 3bc + 6b2 + 2c2) = 0

Combine like terms: 4bc + 3bc = 7bc
(7bc + 6b2 + 2c2) = 0

Solving
7bc + 6b2 + 2c2 = 0

Solving for variable 'b'.

Factor a trinomial.
(2b + c)(3b + 2c) = 0

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

Simplifying
2b + c = 0

Solving
2b + c = 0

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

Add '-1c' to each side of the equation.
2b + c + -1c = 0 + -1c

Combine like terms: c + -1c = 0
2b + 0 = 0 + -1c
2b = 0 + -1c
Remove the zero:
2b = -1c

Divide each side by '2'.
b = -0.5c

Simplifying
b = -0.5c
Subproblem 2
Set the factor '(3b + 2c)' equal to zero and attempt to solve:

Simplifying
3b + 2c = 0

Solving
3b + 2c = 0

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

Add '-2c' to each side of the equation.
3b + 2c + -2c = 0 + -2c

Combine like terms: 2c + -2c = 0
3b + 0 = 0 + -2c
3b = 0 + -2c
Remove the zero:
3b = -2c

Divide each side by '3'.
b = -0.6666666667c

Simplifying
b = -0.6666666667c
Solution
b = {-0.5c, -0.6666666667c}