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

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


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

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

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

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

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

Solving
-4ab + 6a2 + -2b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-2ab + 3a2 + -1b2) = 0

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

Ignore the factor 2.

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

Simplifying
a + -1b = 0

Solving
a + -1b = 0

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

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

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

Simplifying
a = b

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 = {b, -0.3333333333b}

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