(3y+1)(3y+1)=100

Solution for (3y+1)(3y+1)=100 equation:

Simplifying
(3y + 1)(3y + 1) = 100

Reorder the terms:
(1 + 3y)(3y + 1) = 100

Reorder the terms:
(1 + 3y)(1 + 3y) = 100

Multiply (1 + 3y) * (1 + 3y)
(1(1 + 3y) + 3y * (1 + 3y)) = 100
((1 * 1 + 3y * 1) + 3y * (1 + 3y)) = 100
((1 + 3y) + 3y * (1 + 3y)) = 100
(1 + 3y + (1 * 3y + 3y * 3y)) = 100
(1 + 3y + (3y + 9y2)) = 100

Combine like terms: 3y + 3y = 6y
(1 + 6y + 9y2) = 100

Solving
1 + 6y + 9y2 = 100

Solving for variable 'y'.

Reorder the terms:
1 + -100 + 6y + 9y2 = 100 + -100

Combine like terms: 1 + -100 = -99
-99 + 6y + 9y2 = 100 + -100

Combine like terms: 100 + -100 = 0
-99 + 6y + 9y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-33 + 2y + 3y2) = 0

Factor a trinomial.
3((-11 + -3y)(3 + -1y)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-11 + -3y)' equal to zero and attempt to solve:

Simplifying
-11 + -3y = 0

Solving
-11 + -3y = 0

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

Add '11' to each side of the equation.
-11 + 11 + -3y = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -3y = 0 + 11
-3y = 0 + 11

Combine like terms: 0 + 11 = 11
-3y = 11

Divide each side by '-3'.
y = -3.666666667

Simplifying
y = -3.666666667
Subproblem 2
Set the factor '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Solution
y = {-3.666666667, 3}