(2b-3na)(b-3na)=

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Solution for (2b-3na)(b-3na)= equation: 


Simplifying
(2b + -3na)(b + -3na) = 0

Reorder the terms:
(-3an + 2b)(b + -3na) = 0

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

Multiply (-3an + 2b) * (-3an + b)
(-3an * (-3an + b) + 2b * (-3an + b)) = 0
((-3an * -3an + b * -3an) + 2b * (-3an + b)) = 0

Reorder the terms:
((-3abn + 9a2n2) + 2b * (-3an + b)) = 0
((-3abn + 9a2n2) + 2b * (-3an + b)) = 0
(-3abn + 9a2n2 + (-3an * 2b + b * 2b)) = 0
(-3abn + 9a2n2 + (-6abn + 2b2)) = 0

Reorder the terms:
(-3abn + -6abn + 9a2n2 + 2b2) = 0

Combine like terms: -3abn + -6abn = -9abn
(-9abn + 9a2n2 + 2b2) = 0

Solving
-9abn + 9a2n2 + 2b2 = 0

Solving for variable 'a'.

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


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

Simplifying
3an + -2b = 0

Solving
3an + -2b = 0

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

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

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

Divide each side by '3n'.
a = 0.6666666667bn-1

Simplifying
a = 0.6666666667bn-1

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

Simplifying
3an + -1b = 0

Solving
3an + -1b = 0

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

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

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

Divide each side by '3n'.
a = 0.3333333333bn-1

Simplifying
a = 0.3333333333bn-1
Solution
a = {0.6666666667bn-1, 0.3333333333bn-1}

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