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

Solution for (4a+2b)(a-b)=0 equation:

Simplifying
(4a + 2b)(a + -1b) = 0

Multiply (4a + 2b) * (a + -1b)
(4a * (a + -1b) + 2b * (a + -1b)) = 0
((a * 4a + -1b * 4a) + 2b * (a + -1b)) = 0

Reorder the terms:
((-4ab + 4a2) + 2b * (a + -1b)) = 0
((-4ab + 4a2) + 2b * (a + -1b)) = 0
(-4ab + 4a2 + (a * 2b + -1b * 2b)) = 0
(-4ab + 4a2 + (2ab + -2b2)) = 0

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

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

Solving
-2ab + 4a2 + -2b2 = 0

Solving for variable 'a'.

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

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

Ignore the factor 2.
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 '(2a + b)' equal to zero and attempt to solve:

Simplifying
2a + b = 0

Solving
2a + b = 0

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

Add '-1b' to each side of the equation.
2a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
2a + 0 = 0 + -1b
2a = 0 + -1b
Remove the zero:
2a = -1b

Divide each side by '2'.
a = -0.5b

Simplifying
a = -0.5b
Solution
a = {b, -0.5b}