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

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

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

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

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

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

Ignore the factor 2.
Subproblem 1
Set the factor '(2a + -1b)' equal to zero and attempt to solve:

Simplifying
2a + -1b = 0

Solving
2a + -1b = 0

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

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

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

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

Simplifying
a = 0.5b
Subproblem 2
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
Solution
a = {0.5b, -1b}