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

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

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

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

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

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

Combine like terms: -3abc + 2abc = -1abc
(-1abc + a2b2 + -6c2) = 0

Solving
-1abc + a2b2 + -6c2 = 0

Solving for variable 'a'.

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

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