=(a+2)(b+3)

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

Simplifying
0 = (a + 2)(b + 3)

Reorder the terms:
0 = (2 + a)(b + 3)

Reorder the terms:
0 = (2 + a)(3 + b)

Multiply (2 + a) * (3 + b)
0 = (2(3 + b) + a(3 + b))
0 = ((3 * 2 + b * 2) + a(3 + b))
0 = ((6 + 2b) + a(3 + b))
0 = (6 + 2b + (3 * a + b * a))
0 = (6 + 2b + (3a + ab))

Reorder the terms:
0 = (6 + 3a + ab + 2b)
0 = (6 + 3a + ab + 2b)

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

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 = 6 + 3a + ab + -3a + 2b
Remove the zero:
-3a = 6 + 3a + ab + -3a + 2b

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

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

Add '-1ab' to each side of the equation.
-3a + -1ab = 6 + ab + -1ab + 2b

Combine like terms: ab + -1ab = 0
-3a + -1ab = 6 + 0 + 2b
-3a + -1ab = 6 + 2b

Reorder the terms:
-6 + -3a + -1ab + -2b = 6 + 2b + -6 + -2b

Reorder the terms:
-6 + -3a + -1ab + -2b = 6 + -6 + 2b + -2b

Combine like terms: 6 + -6 = 0
-6 + -3a + -1ab + -2b = 0 + 2b + -2b
-6 + -3a + -1ab + -2b = 2b + -2b

Combine like terms: 2b + -2b = 0
-6 + -3a + -1ab + -2b = 0

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

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

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

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

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

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

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

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

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

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

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

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.