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

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


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

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

Reorder the terms:
((-12ab + 6a2) + 2b * (2a + -4b)) = 0
((-12ab + 6a2) + 2b * (2a + -4b)) = 0
(-12ab + 6a2 + (2a * 2b + -4b * 2b)) = 0
(-12ab + 6a2 + (4ab + -8b2)) = 0

Reorder the terms:
(-12ab + 4ab + 6a2 + -8b2) = 0

Combine like terms: -12ab + 4ab = -8ab
(-8ab + 6a2 + -8b2) = 0

Solving
-8ab + 6a2 + -8b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4ab + 3a2 + -4b2) = 0

Factor a trinomial.
2((a + -2b)(3a + 2b)) = 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 + 2b)' equal to zero and attempt to solve:

Simplifying
3a + 2b = 0

Solving
3a + 2b = 0

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

Add '-2b' to each side of the equation.
3a + 2b + -2b = 0 + -2b

Combine like terms: 2b + -2b = 0
3a + 0 = 0 + -2b
3a = 0 + -2b
Remove the zero:
3a = -2b

Divide each side by '3'.
a = -0.6666666667b

Simplifying
a = -0.6666666667b
Solution
a = {2b, -0.6666666667b}

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