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

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


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

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

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

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

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

Solving
-2ab + 2a2 + -12b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1ab + a2 + -6b2) = 0

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

Ignore the factor 2.

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

Simplifying
a + -3b = 0

Solving
a + -3b = 0

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

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

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

Simplifying
a = 3b

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 = {3b, -2b}

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