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

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

Simplifying
(-1a + -2b)(a + 3b) = 0

Multiply (-1a + -2b) * (a + 3b)
(-1a * (a + 3b) + -2b * (a + 3b)) = 0
((a * -1a + 3b * -1a) + -2b * (a + 3b)) = 0

Reorder the terms:
((-3ab + -1a2) + -2b * (a + 3b)) = 0
((-3ab + -1a2) + -2b * (a + 3b)) = 0
(-3ab + -1a2 + (a * -2b + 3b * -2b)) = 0
(-3ab + -1a2 + (-2ab + -6b2)) = 0

Reorder the terms:
(-3ab + -2ab + -1a2 + -6b2) = 0

Combine like terms: -3ab + -2ab = -5ab
(-5ab + -1a2 + -6b2) = 0

Solving
-5ab + -1a2 + -6b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5ab + a2 + 6b2) = 0

Factor a trinomial.
-1((a + 2b)(a + 3b)) = 0

Ignore the factor -1.
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}