(a+3b)(3a-6b)=0

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Solution for (a+3b)(3a-6b)=0 equation: 


Simplifying
(a + 3b)(3a + -6b) = 0

Multiply (a + 3b) * (3a + -6b)
(a(3a + -6b) + 3b * (3a + -6b)) = 0
((3a * a + -6b * a) + 3b * (3a + -6b)) = 0

Reorder the terms:
((-6ab + 3a2) + 3b * (3a + -6b)) = 0
((-6ab + 3a2) + 3b * (3a + -6b)) = 0
(-6ab + 3a2 + (3a * 3b + -6b * 3b)) = 0
(-6ab + 3a2 + (9ab + -18b2)) = 0

Reorder the terms:
(-6ab + 9ab + 3a2 + -18b2) = 0

Combine like terms: -6ab + 9ab = 3ab
(3ab + 3a2 + -18b2) = 0

Solving
3ab + 3a2 + -18b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(ab + a2 + -6b2) = 0

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

Ignore the factor 3.

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 '(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
Solution
a = {2b, -3b}

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