(3y-1)(3y-1)=16

Solution for (3y-1)(3y-1)=16 equation:

Simplifying
(3y + -1)(3y + -1) = 16

Reorder the terms:
(-1 + 3y)(3y + -1) = 16

Reorder the terms:
(-1 + 3y)(-1 + 3y) = 16

Multiply (-1 + 3y) * (-1 + 3y)
(-1(-1 + 3y) + 3y * (-1 + 3y)) = 16
((-1 * -1 + 3y * -1) + 3y * (-1 + 3y)) = 16
((1 + -3y) + 3y * (-1 + 3y)) = 16
(1 + -3y + (-1 * 3y + 3y * 3y)) = 16
(1 + -3y + (-3y + 9y2)) = 16

Combine like terms: -3y + -3y = -6y
(1 + -6y + 9y2) = 16

Solving
1 + -6y + 9y2 = 16

Solving for variable 'y'.

Reorder the terms:
1 + -16 + -6y + 9y2 = 16 + -16

Combine like terms: 1 + -16 = -15
-15 + -6y + 9y2 = 16 + -16

Combine like terms: 16 + -16 = 0
-15 + -6y + 9y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + -2y + 3y2) = 0

Factor a trinomial.
3((-1 + -1y)(5 + -3y)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + -1y)' equal to zero and attempt to solve:

Simplifying
-1 + -1y = 0

Solving
-1 + -1y = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1y = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1y = 0 + 1
-1y = 0 + 1

Combine like terms: 0 + 1 = 1
-1y = 1

Divide each side by '-1'.
y = -1

Simplifying
y = -1
Subproblem 2
Set the factor '(5 + -3y)' equal to zero and attempt to solve:

Simplifying
5 + -3y = 0

Solving
5 + -3y = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3y = 0 + -5
-3y = 0 + -5

Combine like terms: 0 + -5 = -5
-3y = -5

Divide each side by '-3'.
y = 1.666666667

Simplifying
y = 1.666666667
Solution
y = {-1, 1.666666667}