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

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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}

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