(a-b)(a+2b)=0

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

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

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

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

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

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

Solving
1ab + a2 + -2b2 = 0

Solving for variable 'a'.

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

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

Simplifying
a + -1b = 0

Solving
a + -1b = 0

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

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

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

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