(-2b-3a)(-a-6b)=0

Solution for (-2b-3a)(-a-6b)=0 equation:

Simplifying
(-2b + -3a)(-1a + -6b) = 0

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

Multiply (-3a + -2b) * (-1a + -6b)
(-3a * (-1a + -6b) + -2b * (-1a + -6b)) = 0
((-1a * -3a + -6b * -3a) + -2b * (-1a + -6b)) = 0

Reorder the terms:
((18ab + 3a2) + -2b * (-1a + -6b)) = 0
((18ab + 3a2) + -2b * (-1a + -6b)) = 0
(18ab + 3a2 + (-1a * -2b + -6b * -2b)) = 0
(18ab + 3a2 + (2ab + 12b2)) = 0

Reorder the terms:
(18ab + 2ab + 3a2 + 12b2) = 0

Combine like terms: 18ab + 2ab = 20ab
(20ab + 3a2 + 12b2) = 0

Solving
20ab + 3a2 + 12b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(3a + 2b)(a + 6b) = 0

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

Simplifying
3a + 2b = 0

Solving
3a + 2b = 0

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

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

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

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

Simplifying
a = -0.6666666667b
Subproblem 2
Set the factor '(a + 6b)' equal to zero and attempt to solve:

Simplifying
a + 6b = 0

Solving
a + 6b = 0

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

Add '-6b' to each side of the equation.
a + 6b + -6b = 0 + -6b

Combine like terms: 6b + -6b = 0
a + 0 = 0 + -6b
a = 0 + -6b
Remove the zero:
a = -6b

Simplifying
a = -6b
Solution
a = {-0.6666666667b, -6b}