8(3a-b)4(2b-a)=

Solution for 8(3a-b)4(2b-a)= equation:

Simplifying
8(3a + -1b) * 4(2b + -1a) = 0

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

Reorder the terms for easier multiplication:
8 * 4(3a + -1b)(-1a + 2b) = 0

Multiply 8 * 4
32(3a + -1b)(-1a + 2b) = 0

Multiply (3a + -1b) * (-1a + 2b)
32(3a * (-1a + 2b) + -1b * (-1a + 2b)) = 0
32((-1a * 3a + 2b * 3a) + -1b * (-1a + 2b)) = 0

Reorder the terms:
32((6ab + -3a2) + -1b * (-1a + 2b)) = 0
32((6ab + -3a2) + -1b * (-1a + 2b)) = 0
32(6ab + -3a2 + (-1a * -1b + 2b * -1b)) = 0
32(6ab + -3a2 + (1ab + -2b2)) = 0

Reorder the terms:
32(6ab + 1ab + -3a2 + -2b2) = 0

Combine like terms: 6ab + 1ab = 7ab
32(7ab + -3a2 + -2b2) = 0
(7ab * 32 + -3a2 * 32 + -2b2 * 32) = 0
(224ab + -96a2 + -64b2) = 0

Solving
224ab + -96a2 + -64b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '32'.
32(7ab + -3a2 + -2b2) = 0

Factor a trinomial.
32((-3a + b)(a + -2b)) = 0

Ignore the factor 32.
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 '(a + -2b)' equal to zero and attempt to solve:

Simplifying
a + -2b = 0

Solving
a + -2b = 0

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

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

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

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