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

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

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

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

Reorder the terms:
((-1ab + 2a2) + 4b * (2a + -1b)) = 0
((-1ab + 2a2) + 4b * (2a + -1b)) = 0
(-1ab + 2a2 + (2a * 4b + -1b * 4b)) = 0
(-1ab + 2a2 + (8ab + -4b2)) = 0

Reorder the terms:
(-1ab + 8ab + 2a2 + -4b2) = 0

Combine like terms: -1ab + 8ab = 7ab
(7ab + 2a2 + -4b2) = 0

Solving
7ab + 2a2 + -4b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(2a + -1b)(a + 4b) = 0

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 + 4b)' equal to zero and attempt to solve:

Simplifying
a + 4b = 0

Solving
a + 4b = 0

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

Add '-4b' to each side of the equation.
a + 4b + -4b = 0 + -4b

Combine like terms: 4b + -4b = 0
a + 0 = 0 + -4b
a = 0 + -4b
Remove the zero:
a = -4b

Simplifying
a = -4b
Solution
a = {0.5b, -4b}