(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 = -14ab
(-14ab + -6a2 + -4b2) = 0

Solving
-14ab + -6a2 + -4b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '-2'.
-2(7ab + 3a2 + 2b2) = 0

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

Ignore the factor -2.

Subproblem 1
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

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

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