(ab+3c)(ab+2c)=

Solution for (ab+3c)(ab+2c)= equation:

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

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

Reorder the terms:
((2abc + a2b2) + 3c * (ab + 2c)) = 0
((2abc + a2b2) + 3c * (ab + 2c)) = 0
(2abc + a2b2 + (ab * 3c + 2c * 3c)) = 0
(2abc + a2b2 + (3abc + 6c2)) = 0

Reorder the terms:
(2abc + 3abc + a2b2 + 6c2) = 0

Combine like terms: 2abc + 3abc = 5abc
(5abc + a2b2 + 6c2) = 0

Solving
5abc + a2b2 + 6c2 = 0

Solving for variable 'a'.

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

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

Simplifying
ab + 2c = 0

Solving
ab + 2c = 0

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

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

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

Divide each side by 'b'.
a = -2b-1c

Simplifying
a = -2b-1c
Subproblem 2
Set the factor '(ab + 3c)' equal to zero and attempt to solve:

Simplifying
ab + 3c = 0

Solving
ab + 3c = 0

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

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

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

Divide each side by 'b'.
a = -3b-1c

Simplifying
a = -3b-1c
Solution
a = {-2b-1c, -3b-1c}