(3y-1)(3y+1)=9

Solution for (3y-1)(3y+1)=9 equation:

Simplifying
(3y + -1)(3y + 1) = 9

Reorder the terms:
(-1 + 3y)(3y + 1) = 9

Reorder the terms:
(-1 + 3y)(1 + 3y) = 9

Multiply (-1 + 3y) * (1 + 3y)
(-1(1 + 3y) + 3y * (1 + 3y)) = 9
((1 * -1 + 3y * -1) + 3y * (1 + 3y)) = 9
((-1 + -3y) + 3y * (1 + 3y)) = 9
(-1 + -3y + (1 * 3y + 3y * 3y)) = 9
(-1 + -3y + (3y + 9y2)) = 9

Combine like terms: -3y + 3y = 0
(-1 + 0 + 9y2) = 9
(-1 + 9y2) = 9

Solving
-1 + 9y2 = 9

Solving for variable 'y'.

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

Add '1' to each side of the equation.
-1 + 1 + 9y2 = 9 + 1

Combine like terms: -1 + 1 = 0
0 + 9y2 = 9 + 1
9y2 = 9 + 1

Combine like terms: 9 + 1 = 10
9y2 = 10

Divide each side by '9'.
y2 = 1.111111111

Simplifying
y2 = 1.111111111

Take the square root of each side:
y = {-1.054092553, 1.054092553}