(3x+2y)(3x-2y)=0

Solution for (3x+2y)(3x-2y)=0 equation:

Simplifying
(3x + 2y)(3x + -2y) = 0

Multiply (3x + 2y) * (3x + -2y)
(3x * (3x + -2y) + 2y * (3x + -2y)) = 0
((3x * 3x + -2y * 3x) + 2y * (3x + -2y)) = 0

Reorder the terms:
((-6xy + 9x2) + 2y * (3x + -2y)) = 0
((-6xy + 9x2) + 2y * (3x + -2y)) = 0
(-6xy + 9x2 + (3x * 2y + -2y * 2y)) = 0
(-6xy + 9x2 + (6xy + -4y2)) = 0

Reorder the terms:
(-6xy + 6xy + 9x2 + -4y2) = 0

Combine like terms: -6xy + 6xy = 0
(0 + 9x2 + -4y2) = 0
(9x2 + -4y2) = 0

Solving
9x2 + -4y2 = 0

Solving for variable 'x'.

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

Add '4y2' to each side of the equation.
9x2 + -4y2 + 4y2 = 0 + 4y2

Combine like terms: -4y2 + 4y2 = 0
9x2 + 0 = 0 + 4y2
9x2 = 0 + 4y2
Remove the zero:
9x2 = 4y2

Divide each side by '9'.
x2 = 0.4444444444y2

Simplifying
x2 = 0.4444444444y2

Take the square root of each side:
x = {-0.666666667y, 0.666666667y}