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

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

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

Reorder the terms:
(2a + -1b)(a + -4a + b) = 0

Combine like terms: a + -4a = -3a
(2a + -1b)(-3a + b) = 0

Multiply (2a + -1b) * (-3a + b)
(2a * (-3a + b) + -1b * (-3a + b)) = 0
((-3a * 2a + b * 2a) + -1b * (-3a + b)) = 0

Reorder the terms:
((2ab + -6a2) + -1b * (-3a + b)) = 0
((2ab + -6a2) + -1b * (-3a + b)) = 0
(2ab + -6a2 + (-3a * -1b + b * -1b)) = 0
(2ab + -6a2 + (3ab + -1b2)) = 0

Reorder the terms:
(2ab + 3ab + -6a2 + -1b2) = 0

Combine like terms: 2ab + 3ab = 5ab
(5ab + -6a2 + -1b2) = 0

Solving
5ab + -6a2 + -1b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-3a + b)(2a + -1b) = 0

Subproblem 1
Set the factor '(-3a + b)' equal to zero and attempt to solve:

Simplifying
-3a + b = 0

Solving
-3a + b = 0

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

Add '-1b' to each side of the equation.
-3a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
-3a + 0 = 0 + -1b
-3a = 0 + -1b
Remove the zero:
-3a = -1b

Divide each side by '-3'.
a = 0.3333333333b

Simplifying
a = 0.3333333333b
Subproblem 2
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
Solution
a = {0.3333333333b, 0.5b}