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

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

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

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

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

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

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

Solving
4x2 + -9y2 = 0

Solving for variable 'x'.

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

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

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

Divide each side by '4'.
x2 = 2.25y2

Simplifying
x2 = 2.25y2

Take the square root of each side:
x = {-1.5y, 1.5y}