ab=(3a+2)(3b+1)

Solution for ab=(3a+2)(3b+1) equation:

Simplifying
ab = (3a + 2)(3b + 1)

Reorder the terms:
ab = (2 + 3a)(3b + 1)

Reorder the terms:
ab = (2 + 3a)(1 + 3b)

Multiply (2 + 3a) * (1 + 3b)
ab = (2(1 + 3b) + 3a * (1 + 3b))
ab = ((1 * 2 + 3b * 2) + 3a * (1 + 3b))
ab = ((2 + 6b) + 3a * (1 + 3b))
ab = (2 + 6b + (1 * 3a + 3b * 3a))
ab = (2 + 6b + (3a + 9ab))

Reorder the terms:
ab = (2 + 3a + 9ab + 6b)
ab = (2 + 3a + 9ab + 6b)

Solving
ab = 2 + 3a + 9ab + 6b

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.
-3a + ab = 2 + 3a + 9ab + -3a + 6b

Reorder the terms:
-3a + ab = 2 + 3a + -3a + 9ab + 6b

Combine like terms: 3a + -3a = 0
-3a + ab = 2 + 0 + 9ab + 6b
-3a + ab = 2 + 9ab + 6b

Add '-9ab' to each side of the equation.
-3a + ab + -9ab = 2 + 9ab + -9ab + 6b

Combine like terms: ab + -9ab = -8ab
-3a + -8ab = 2 + 9ab + -9ab + 6b

Combine like terms: 9ab + -9ab = 0
-3a + -8ab = 2 + 0 + 6b
-3a + -8ab = 2 + 6b

Reorder the terms:
-2 + -3a + -8ab + -6b = 2 + 6b + -2 + -6b

Reorder the terms:
-2 + -3a + -8ab + -6b = 2 + -2 + 6b + -6b

Combine like terms: 2 + -2 = 0
-2 + -3a + -8ab + -6b = 0 + 6b + -6b
-2 + -3a + -8ab + -6b = 6b + -6b

Combine like terms: 6b + -6b = 0
-2 + -3a + -8ab + -6b = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2 + 3a + 8ab + 6b) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(2 + 3a + 8ab + 6b)' equal to zero and attempt to solve:

Simplifying
2 + 3a + 8ab + 6b = 0

Solving
2 + 3a + 8ab + 6b = 0

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

Add '-2' to each side of the equation.
2 + 3a + 8ab + -2 + 6b = 0 + -2

Reorder the terms:
2 + -2 + 3a + 8ab + 6b = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3a + 8ab + 6b = 0 + -2
3a + 8ab + 6b = 0 + -2

Combine like terms: 0 + -2 = -2
3a + 8ab + 6b = -2

Add '-6b' to each side of the equation.
3a + 8ab + 6b + -6b = -2 + -6b

Combine like terms: 6b + -6b = 0
3a + 8ab + 0 = -2 + -6b
3a + 8ab = -2 + -6b

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.