(2a+4b)(a+b)=

Solution for (2a+4b)(a+b)= equation:

Simplifying
(2a + 4b)(a + b) = 0

Multiply (2a + 4b) * (a + b)
(2a * (a + b) + 4b * (a + b)) = 0
((a * 2a + b * 2a) + 4b * (a + b)) = 0

Reorder the terms:
((2ab + 2a2) + 4b * (a + b)) = 0
((2ab + 2a2) + 4b * (a + b)) = 0
(2ab + 2a2 + (a * 4b + b * 4b)) = 0
(2ab + 2a2 + (4ab + 4b2)) = 0

Reorder the terms:
(2ab + 4ab + 2a2 + 4b2) = 0

Combine like terms: 2ab + 4ab = 6ab
(6ab + 2a2 + 4b2) = 0

Solving
6ab + 2a2 + 4b2 = 0

Solving for variable 'a'.

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

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

Ignore the factor 2.
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}