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

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


Simplifying
(2a + 4b)(3a + -1b) = 0

Multiply (2a + 4b) * (3a + -1b)
(2a * (3a + -1b) + 4b * (3a + -1b)) = 0
((3a * 2a + -1b * 2a) + 4b * (3a + -1b)) = 0

Reorder the terms:
((-2ab + 6a2) + 4b * (3a + -1b)) = 0
((-2ab + 6a2) + 4b * (3a + -1b)) = 0
(-2ab + 6a2 + (3a * 4b + -1b * 4b)) = 0
(-2ab + 6a2 + (12ab + -4b2)) = 0

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

Combine like terms: -2ab + 12ab = 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((3a + -1b)(a + 2b)) = 0

Ignore the factor 2.

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

Simplifying
3a + -1b = 0

Solving
3a + -1b = 0

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

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

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

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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