(2a+3b)(6a+9b)=

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Solution for (2a+3b)(6a+9b)= equation: 


Simplifying
(2a + 3b)(6a + 9b) = 0

Multiply (2a + 3b) * (6a + 9b)
(2a * (6a + 9b) + 3b * (6a + 9b)) = 0
((6a * 2a + 9b * 2a) + 3b * (6a + 9b)) = 0

Reorder the terms:
((18ab + 12a2) + 3b * (6a + 9b)) = 0
((18ab + 12a2) + 3b * (6a + 9b)) = 0
(18ab + 12a2 + (6a * 3b + 9b * 3b)) = 0
(18ab + 12a2 + (18ab + 27b2)) = 0

Reorder the terms:
(18ab + 18ab + 12a2 + 27b2) = 0

Combine like terms: 18ab + 18ab = 36ab
(36ab + 12a2 + 27b2) = 0

Solving
36ab + 12a2 + 27b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(12ab + 4a2 + 9b2) = 0

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

Ignore the factor 3.

Subproblem 1
Set the factor '(2a + 3b)' equal to zero and attempt to solve:

Simplifying
2a + 3b = 0

Solving
2a + 3b = 0

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

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

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

Divide each side by '2'.
a = -1.5b

Simplifying
a = -1.5b

Subproblem 2
Set the factor '(2a + 3b)' equal to zero and attempt to solve:

Simplifying
2a + 3b = 0

Solving
2a + 3b = 0

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

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

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

Divide each side by '2'.
a = -1.5b

Simplifying
a = -1.5b
Solution
a = {-1.5b, -1.5b}

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