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

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

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

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

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

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

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

Solving
-3ab + -1a2 + -2b2 = 0

Solving for variable 'a'.

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}