(a+2b)*(a+b)=

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

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

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

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

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

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

Solving
3ab + a2 + 2b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(a + b)(a + 2b) = 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 + 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 = {-1b, -2b}