x(6b-a)=a(x-2b)

Solution for x(6b-a)=a(x-2b) equation:

Simplifying
x(6b + -1a) = a(x + -2b)

Reorder the terms:
x(-1a + 6b) = a(x + -2b)
(-1a * x + 6b * x) = a(x + -2b)
(-1ax + 6bx) = a(x + -2b)

Reorder the terms:
-1ax + 6bx = a(-2b + x)
-1ax + 6bx = (-2b * a + x * a)
-1ax + 6bx = (-2ab + ax)

Solving
-1ax + 6bx = -2ab + ax

Solving for variable 'a'.

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

Add '2ab' to each side of the equation.
-1ax + 2ab + 6bx = -2ab + 2ab + ax

Reorder the terms:
2ab + -1ax + 6bx = -2ab + 2ab + ax

Combine like terms: -2ab + 2ab = 0
2ab + -1ax + 6bx = 0 + ax
2ab + -1ax + 6bx = ax

Add '-1ax' to each side of the equation.
2ab + -1ax + -1ax + 6bx = ax + -1ax

Combine like terms: -1ax + -1ax = -2ax
2ab + -2ax + 6bx = ax + -1ax

Combine like terms: ax + -1ax = 0
2ab + -2ax + 6bx = 0

Add '-6bx' to each side of the equation.
2ab + -2ax + 6bx + -6bx = 0 + -6bx

Combine like terms: 6bx + -6bx = 0
2ab + -2ax + 0 = 0 + -6bx
2ab + -2ax = 0 + -6bx
Remove the zero:
2ab + -2ax = -6bx

Combine like terms: -6bx + 6bx = 0
2ab + -2ax + 6bx = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(ab + -1ax + 3bx) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(ab + -1ax + 3bx)' equal to zero and attempt to solve:

Simplifying
ab + -1ax + 3bx = 0

Solving
ab + -1ax + 3bx = 0

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

Add '-3bx' to each side of the equation.
ab + -1ax + 3bx + -3bx = 0 + -3bx

Combine like terms: 3bx + -3bx = 0
ab + -1ax + 0 = 0 + -3bx
ab + -1ax = 0 + -3bx
Remove the zero:
ab + -1ax = -3bx

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.