(a+2b)(a+3b)=

Solution for (a+2b)(a+3b)= equation:

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

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

Reorder the terms:
((3ab + a2) + 2b * (a + 3b)) = 0
((3ab + a2) + 2b * (a + 3b)) = 0
(3ab + a2 + (a * 2b + 3b * 2b)) = 0
(3ab + a2 + (2ab + 6b2)) = 0

Reorder the terms:
(3ab + 2ab + a2 + 6b2) = 0

Combine like terms: 3ab + 2ab = 5ab
(5ab + a2 + 6b2) = 0

Solving
5ab + a2 + 6b2 = 0

Solving for variable 'a'.

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

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

Simplifying
a + 2b = 0

Solving
a + 2b = 0

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

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

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

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

Simplifying
a + 3b = 0

Solving
a + 3b = 0

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

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

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

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