(2x+3y)(6x+9y)=

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Solution for (2x+3y)(6x+9y)= equation: 


Simplifying
(2x + 3y)(6x + 9y) = 0

Multiply (2x + 3y) * (6x + 9y)
(2x * (6x + 9y) + 3y * (6x + 9y)) = 0
((6x * 2x + 9y * 2x) + 3y * (6x + 9y)) = 0

Reorder the terms:
((18xy + 12x2) + 3y * (6x + 9y)) = 0
((18xy + 12x2) + 3y * (6x + 9y)) = 0
(18xy + 12x2 + (6x * 3y + 9y * 3y)) = 0
(18xy + 12x2 + (18xy + 27y2)) = 0

Reorder the terms:
(18xy + 18xy + 12x2 + 27y2) = 0

Combine like terms: 18xy + 18xy = 36xy
(36xy + 12x2 + 27y2) = 0

Solving
36xy + 12x2 + 27y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(12xy + 4x2 + 9y2) = 0

Factor a trinomial.
3((2x + 3y)(2x + 3y)) = 0

Ignore the factor 3.

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

Simplifying
2x + 3y = 0

Solving
2x + 3y = 0

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

Add '-3y' to each side of the equation.
2x + 3y + -3y = 0 + -3y

Combine like terms: 3y + -3y = 0
2x + 0 = 0 + -3y
2x = 0 + -3y
Remove the zero:
2x = -3y

Divide each side by '2'.
x = -1.5y

Simplifying
x = -1.5y

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

Simplifying
2x + 3y = 0

Solving
2x + 3y = 0

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

Add '-3y' to each side of the equation.
2x + 3y + -3y = 0 + -3y

Combine like terms: 3y + -3y = 0
2x + 0 = 0 + -3y
2x = 0 + -3y
Remove the zero:
2x = -3y

Divide each side by '2'.
x = -1.5y

Simplifying
x = -1.5y
Solution
x = {-1.5y, -1.5y}

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