(8x+9y)(8x-9y)=0

Solution for (8x+9y)(8x-9y)=0 equation:

Simplifying
(8x + 9y)(8x + -9y) = 0

Multiply (8x + 9y) * (8x + -9y)
(8x * (8x + -9y) + 9y * (8x + -9y)) = 0
((8x * 8x + -9y * 8x) + 9y * (8x + -9y)) = 0

Reorder the terms:
((-72xy + 64x2) + 9y * (8x + -9y)) = 0
((-72xy + 64x2) + 9y * (8x + -9y)) = 0
(-72xy + 64x2 + (8x * 9y + -9y * 9y)) = 0
(-72xy + 64x2 + (72xy + -81y2)) = 0

Reorder the terms:
(-72xy + 72xy + 64x2 + -81y2) = 0

Combine like terms: -72xy + 72xy = 0
(0 + 64x2 + -81y2) = 0
(64x2 + -81y2) = 0

Solving
64x2 + -81y2 = 0

Solving for variable 'x'.

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

Add '81y2' to each side of the equation.
64x2 + -81y2 + 81y2 = 0 + 81y2

Combine like terms: -81y2 + 81y2 = 0
64x2 + 0 = 0 + 81y2
64x2 = 0 + 81y2
Remove the zero:
64x2 = 81y2

Divide each side by '64'.
x2 = 1.265625y2

Simplifying
x2 = 1.265625y2

Take the square root of each side:
x = {-1.125y, 1.125y}