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

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


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

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

Reorder the terms:
((-3ab + 9a2) + 2b * (3a + -1b)) = 0
((-3ab + 9a2) + 2b * (3a + -1b)) = 0
(-3ab + 9a2 + (3a * 2b + -1b * 2b)) = 0
(-3ab + 9a2 + (6ab + -2b2)) = 0

Reorder the terms:
(-3ab + 6ab + 9a2 + -2b2) = 0

Combine like terms: -3ab + 6ab = 3ab
(3ab + 9a2 + -2b2) = 0

Solving
3ab + 9a2 + -2b2 = 0

Solving for variable 'a'.

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


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

Simplifying
3a + -1b = 0

Solving
3a + -1b = 0

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

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

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

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

Simplifying
a = 0.3333333333b

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

Simplifying
3a + 2b = 0

Solving
3a + 2b = 0

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

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

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

Divide each side by '3'.
a = -0.6666666667b

Simplifying
a = -0.6666666667b
Solution
a = {0.3333333333b, -0.6666666667b}

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