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

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


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

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

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

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

Combine like terms: 3ab + 2ab = 5ab
(5ab + 6a2 + b2) = 0

Solving
5ab + 6a2 + b2 = 0

Solving for variable 'a'.

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


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

Simplifying
3a + b = 0

Solving
3a + b = 0

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

Add '-1b' to each side of the equation.
3a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
3a + 0 = 0 + -1b
3a = 0 + -1b
Remove the zero:
3a = -1b

Divide each side by '3'.
a = -0.3333333333b

Simplifying
a = -0.3333333333b

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

Simplifying
2a + b = 0

Solving
2a + b = 0

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

Add '-1b' to each side of the equation.
2a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
2a + 0 = 0 + -1b
2a = 0 + -1b
Remove the zero:
2a = -1b

Divide each side by '2'.
a = -0.5b

Simplifying
a = -0.5b
Solution
a = {-0.3333333333b, -0.5b}

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