(3a+b)(2a-4b)=0

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Solution for (3a+b)(2a-4b)=0 equation: 


Simplifying
(3a + b)(2a + -4b) = 0

Multiply (3a + b) * (2a + -4b)
(3a * (2a + -4b) + b(2a + -4b)) = 0
((2a * 3a + -4b * 3a) + b(2a + -4b)) = 0

Reorder the terms:
((-12ab + 6a2) + b(2a + -4b)) = 0
((-12ab + 6a2) + b(2a + -4b)) = 0
(-12ab + 6a2 + (2a * b + -4b * b)) = 0
(-12ab + 6a2 + (2ab + -4b2)) = 0

Reorder the terms:
(-12ab + 2ab + 6a2 + -4b2) = 0

Combine like terms: -12ab + 2ab = -10ab
(-10ab + 6a2 + -4b2) = 0

Solving
-10ab + 6a2 + -4b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5ab + 3a2 + -2b2) = 0

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

Ignore the factor 2.

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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