=a(4b-9)+a(6-b)

Solution for =a(4b-9)+a(6-b) equation:

Simplifying
0 = a(4b + -9) + a(6 + -1b)

Reorder the terms:
0 = a(-9 + 4b) + a(6 + -1b)
0 = (-9 * a + 4b * a) + a(6 + -1b)
0 = (-9a + 4ab) + a(6 + -1b)
0 = -9a + 4ab + (6 * a + -1b * a)
0 = -9a + 4ab + (6a + -1ab)

Reorder the terms:
0 = -9a + 6a + 4ab + -1ab

Combine like terms: -9a + 6a = -3a
0 = -3a + 4ab + -1ab

Combine like terms: 4ab + -1ab = 3ab
0 = -3a + 3ab

Solving
0 = -3a + 3ab

Solving for variable 'a'.

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

Add '3a' to each side of the equation.
0 + 3a = -3a + 3a + 3ab
Remove the zero:
3a = -3a + 3a + 3ab

Combine like terms: -3a + 3a = 0
3a = 0 + 3ab
3a = 3ab

Add '-3ab' to each side of the equation.
3a + -3ab = 3ab + -3ab

Combine like terms: 3ab + -3ab = 0
3a + -3ab = 0

Factor out the Greatest Common Factor (GCF), '3a'.
3a(1 + -1b) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
Set the factor '(1 + -1b)' equal to zero and attempt to solve:

Simplifying
1 + -1b = 0

Solving
1 + -1b = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1b = 0 + -1
-1b = 0 + -1

Combine like terms: 0 + -1 = -1
-1b = -1

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

Combine like terms: -1b + b = 0
0 = -1 + b

Simplifying
0 = -1 + b

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
a = {0}