(3y-1)(3y-1)-25=0

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Solution for (3y-1)(3y-1)-25=0 equation: 


Simplifying
(3y + -1)(3y + -1) + -25 = 0

Reorder the terms:
(-1 + 3y)(3y + -1) + -25 = 0

Reorder the terms:
(-1 + 3y)(-1 + 3y) + -25 = 0

Multiply (-1 + 3y) * (-1 + 3y)
(-1(-1 + 3y) + 3y * (-1 + 3y)) + -25 = 0
((-1 * -1 + 3y * -1) + 3y * (-1 + 3y)) + -25 = 0
((1 + -3y) + 3y * (-1 + 3y)) + -25 = 0
(1 + -3y + (-1 * 3y + 3y * 3y)) + -25 = 0
(1 + -3y + (-3y + 9y2)) + -25 = 0

Combine like terms: -3y + -3y = -6y
(1 + -6y + 9y2) + -25 = 0

Reorder the terms:
1 + -25 + -6y + 9y2 = 0

Combine like terms: 1 + -25 = -24
-24 + -6y + 9y2 = 0

Solving
-24 + -6y + 9y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + -2y + 3y2) = 0

Factor a trinomial.
3((-4 + -3y)(2 + -1y)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-4 + -3y)' equal to zero and attempt to solve:

Simplifying
-4 + -3y = 0

Solving
-4 + -3y = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3y = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3y = 0 + 4
-3y = 0 + 4

Combine like terms: 0 + 4 = 4
-3y = 4

Divide each side by '-3'.
y = -1.333333333

Simplifying
y = -1.333333333

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

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1y = 0 + -2
-1y = 0 + -2

Combine like terms: 0 + -2 = -2
-1y = -2

Divide each side by '-1'.
y = 2

Simplifying
y = 2
Solution
y = {-1.333333333, 2}

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