(3a-b)x(a+6b)=

Solution for (3a-b)x(a+6b)= equation:

Simplifying
(3a + -1b) * x(a + 6b) = 0

Reorder the terms for easier multiplication:
x(3a + -1b)(a + 6b) = 0

Multiply (3a + -1b) * (a + 6b)
x(3a * (a + 6b) + -1b * (a + 6b)) = 0
x((a * 3a + 6b * 3a) + -1b * (a + 6b)) = 0

Reorder the terms:
x((18ab + 3a2) + -1b * (a + 6b)) = 0
x((18ab + 3a2) + -1b * (a + 6b)) = 0
x(18ab + 3a2 + (a * -1b + 6b * -1b)) = 0
x(18ab + 3a2 + (-1ab + -6b2)) = 0

Reorder the terms:
x(18ab + -1ab + 3a2 + -6b2) = 0

Combine like terms: 18ab + -1ab = 17ab
x(17ab + 3a2 + -6b2) = 0
(17ab * x + 3a2 * x + -6b2 * x) = 0
(17abx + 3a2x + -6b2x) = 0

Solving
17abx + 3a2x + -6b2x = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(17ab + 3a2 + -6b2) = 0

Factor a trinomial.
x((3a + -1b)(a + 6b)) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Add '-1x' to each side of the equation.
x + -1x = 0 + -1x
Remove the zero:
0 = -1x

Simplifying
0 = -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(3a + -1b)' equal to zero and attempt to solve:

Simplifying
3a + -1b = 0

Solving
3a + -1b = 0

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

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

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

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

Simplifying
a = 0.3333333333b
Subproblem 3
Set the factor '(a + 6b)' equal to zero and attempt to solve:

Simplifying
a + 6b = 0

Solving
a + 6b = 0

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

Add '-6b' to each side of the equation.
a + 6b + -6b = 0 + -6b

Combine like terms: 6b + -6b = 0
a + 0 = 0 + -6b
a = 0 + -6b
Remove the zero:
a = -6b

Simplifying
a = -6b
Solution
a = {0.3333333333b, -6b}