(2a-3b)(4a-b)=

Solution for (2a-3b)(4a-b)= equation:

Simplifying
(2a + -3b)(4a + -1b) = 0

Multiply (2a + -3b) * (4a + -1b)
(2a * (4a + -1b) + -3b * (4a + -1b)) = 0
((4a * 2a + -1b * 2a) + -3b * (4a + -1b)) = 0

Reorder the terms:
((-2ab + 8a2) + -3b * (4a + -1b)) = 0
((-2ab + 8a2) + -3b * (4a + -1b)) = 0
(-2ab + 8a2 + (4a * -3b + -1b * -3b)) = 0
(-2ab + 8a2 + (-12ab + 3b2)) = 0

Reorder the terms:
(-2ab + -12ab + 8a2 + 3b2) = 0

Combine like terms: -2ab + -12ab = -14ab
(-14ab + 8a2 + 3b2) = 0

Solving
-14ab + 8a2 + 3b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(2a + -3b)(4a + -1b) = 0

Subproblem 1
Set the factor '(2a + -3b)' equal to zero and attempt to solve:

Simplifying
2a + -3b = 0

Solving
2a + -3b = 0

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

Add '3b' to each side of the equation.
2a + -3b + 3b = 0 + 3b

Combine like terms: -3b + 3b = 0
2a + 0 = 0 + 3b
2a = 0 + 3b
Remove the zero:
2a = 3b

Divide each side by '2'.
a = 1.5b

Simplifying
a = 1.5b
Subproblem 2
Set the factor '(4a + -1b)' equal to zero and attempt to solve:

Simplifying
4a + -1b = 0

Solving
4a + -1b = 0

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

Add 'b' to each side of the equation.
4a + -1b + b = 0 + b

Combine like terms: -1b + b = 0
4a + 0 = 0 + b
4a = 0 + b
Remove the zero:
4a = b

Divide each side by '4'.
a = 0.25b

Simplifying
a = 0.25b
Solution
a = {1.5b, 0.25b}