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

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

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

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

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

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

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

Solving
0 = 3ab + a2 + 2b2

Solving for variable 'a'.
Remove the zero:
-3ab + -1a2 + -2b2 = 3ab + a2 + 2b2 + -3ab + -1a2 + -2b2

Reorder the terms:
-3ab + -1a2 + -2b2 = 3ab + -3ab + a2 + -1a2 + 2b2 + -2b2

Combine like terms: 3ab + -3ab = 0
-3ab + -1a2 + -2b2 = 0 + a2 + -1a2 + 2b2 + -2b2
-3ab + -1a2 + -2b2 = a2 + -1a2 + 2b2 + -2b2

Combine like terms: a2 + -1a2 = 0
-3ab + -1a2 + -2b2 = 0 + 2b2 + -2b2
-3ab + -1a2 + -2b2 = 2b2 + -2b2

Combine like terms: 2b2 + -2b2 = 0
-3ab + -1a2 + -2b2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3ab + a2 + 2b2) = 0

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

Ignore the factor -1.
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}