90y^2-216y+108=0

Solution for 90y^2-216y+108=0 equation:

Simplifying
90y2 + -216y + 108 = 0

Reorder the terms:
108 + -216y + 90y2 = 0

Solving
108 + -216y + 90y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '18'.
18(6 + -12y + 5y2) = 0

Ignore the factor 18.
Subproblem 1
Set the factor '(6 + -12y + 5y2)' equal to zero and attempt to solve:

Simplifying
6 + -12y + 5y2 = 0

Solving
6 + -12y + 5y2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
1.2 + -2.4y + y2 = 0

Move the constant term to the right:

Add '-1.2' to each side of the equation.
1.2 + -2.4y + -1.2 + y2 = 0 + -1.2

Reorder the terms:
1.2 + -1.2 + -2.4y + y2 = 0 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + -2.4y + y2 = 0 + -1.2
-2.4y + y2 = 0 + -1.2

Combine like terms: 0 + -1.2 = -1.2
-2.4y + y2 = -1.2

The y term is -2.4y.  Take half its coefficient (-1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
-2.4y + 1.44 + y2 = -1.2 + 1.44

Reorder the terms:
1.44 + -2.4y + y2 = -1.2 + 1.44

Combine like terms: -1.2 + 1.44 = 0.24
1.44 + -2.4y + y2 = 0.24

Factor a perfect square on the left side:
(y + -1.2)(y + -1.2) = 0.24

Calculate the square root of the right side: 0.489897949

Break this problem into two subproblems by setting 
(y + -1.2) equal to 0.489897949 and -0.489897949.

Subproblem 1
y + -1.2 = 0.489897949

Simplifying
y + -1.2 = 0.489897949

Reorder the terms:
-1.2 + y = 0.489897949

Solving
-1.2 + y = 0.489897949

Solving for variable 'y'.

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

Add '1.2' to each side of the equation.
-1.2 + 1.2 + y = 0.489897949 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + y = 0.489897949 + 1.2
y = 0.489897949 + 1.2

Combine like terms: 0.489897949 + 1.2 = 1.689897949
y = 1.689897949

Simplifying
y = 1.689897949

Subproblem 2
y + -1.2 = -0.489897949

Simplifying
y + -1.2 = -0.489897949

Reorder the terms:
-1.2 + y = -0.489897949

Solving
-1.2 + y = -0.489897949

Solving for variable 'y'.

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

Add '1.2' to each side of the equation.
-1.2 + 1.2 + y = -0.489897949 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + y = -0.489897949 + 1.2
y = -0.489897949 + 1.2

Combine like terms: -0.489897949 + 1.2 = 0.710102051
y = 0.710102051

Simplifying
y = 0.710102051

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.689897949, 0.710102051}
Solution
y = {1.689897949, 0.710102051}