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

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

Simplifying
0 = (2b + 1a)(3b + 2a)

Reorder the terms:
0 = (1a + 2b)(3b + 2a)

Reorder the terms:
0 = (1a + 2b)(2a + 3b)

Multiply (1a + 2b) * (2a + 3b)
0 = (1a * (2a + 3b) + 2b * (2a + 3b))
0 = ((2a * 1a + 3b * 1a) + 2b * (2a + 3b))

Reorder the terms:
0 = ((3ab + 2a2) + 2b * (2a + 3b))
0 = ((3ab + 2a2) + 2b * (2a + 3b))
0 = (3ab + 2a2 + (2a * 2b + 3b * 2b))
0 = (3ab + 2a2 + (4ab + 6b2))

Reorder the terms:
0 = (3ab + 4ab + 2a2 + 6b2)

Combine like terms: 3ab + 4ab = 7ab
0 = (7ab + 2a2 + 6b2)

Solving
0 = 7ab + 2a2 + 6b2

Solving for variable 'a'.
Remove the zero:
-7ab + -2a2 + -6b2 = 7ab + 2a2 + 6b2 + -7ab + -2a2 + -6b2

Reorder the terms:
-7ab + -2a2 + -6b2 = 7ab + -7ab + 2a2 + -2a2 + 6b2 + -6b2

Combine like terms: 7ab + -7ab = 0
-7ab + -2a2 + -6b2 = 0 + 2a2 + -2a2 + 6b2 + -6b2
-7ab + -2a2 + -6b2 = 2a2 + -2a2 + 6b2 + -6b2

Combine like terms: 2a2 + -2a2 = 0
-7ab + -2a2 + -6b2 = 0 + 6b2 + -6b2
-7ab + -2a2 + -6b2 = 6b2 + -6b2

Combine like terms: 6b2 + -6b2 = 0
-7ab + -2a2 + -6b2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(7ab + 2a2 + 6b2) = 0

Factor a trinomial.
-1((2a + 3b)(a + 2b)) = 0

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

Simplifying
2a + 3b = 0

Solving
2a + 3b = 0

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

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

Combine like terms: 3b + -3b = 0
2a + 0 = 0 + -3b
2a = 0 + -3b
Remove the zero:
2a = -3b

Divide each side by '2'.
a = -1.5b

Simplifying
a = -1.5b
Subproblem 2
Set the factor '(a + 2b)' equal to zero and attempt to solve:

Simplifying
a + 2b = 0

Solving
a + 2b = 0

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

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

Combine like terms: 2b + -2b = 0
a + 0 = 0 + -2b
a = 0 + -2b
Remove the zero:
a = -2b

Simplifying
a = -2b
Solution
a = {-1.5b, -2b}