(a+b)(a+6b)=0

Solution for (a+b)(a+6b)=0 equation:

Simplifying
(a + b)(a + 6b) = 0

Multiply (a + b) * (a + 6b)
(a(a + 6b) + b(a + 6b)) = 0
((a * a + 6b * a) + b(a + 6b)) = 0

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

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

Combine like terms: 6ab + ab = 7ab
(7ab + a2 + 6b2) = 0

Solving
7ab + a2 + 6b2 = 0

Solving for variable 'a'.

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

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

Simplifying
a + b = 0

Solving
a + b = 0

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

Add '-1b' to each side of the equation.
a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
a + 0 = 0 + -1b
a = 0 + -1b
Remove the zero:
a = -1b

Simplifying
a = -1b
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 = {-1b, -6b}