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

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


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

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

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

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

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

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

Solving
-5ab + 3a2 + -2b2 = 0

Solving for variable 'a'.

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


Subproblem 1
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

Subproblem 2
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
Solution
a = {2b, -0.3333333333b}

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