1.8y(5-2y)=0.9

Solution for 1.8y(5-2y)=0.9 equation:

Simplifying
1.8y(5 + -2y) = 0.9
(5 * 1.8y + -2y * 1.8y) = 0.9
(9y + -3.6y2) = 0.9

Solving
9y + -3.6y2 = 0.9

Solving for variable 'y'.

Reorder the terms:
-0.9 + 9y + -3.6y2 = 0.9 + -0.9

Combine like terms: 0.9 + -0.9 = 0.0
-0.9 + 9y + -3.6y2 = 0.0

Begin completing the square.  Divide all terms by
-3.6 the coefficient of the squared term: 

Divide each side by '-3.6'.
0.25 + -2.5y + y2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -2.5y + -0.25 + y2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -2.5y + y2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -2.5y + y2 = 0 + -0.25
-2.5y + y2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-2.5y + y2 = -0.25

The y term is -2.5y.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5y + 1.5625 + y2 = -0.25 + 1.5625

Reorder the terms:
1.5625 + -2.5y + y2 = -0.25 + 1.5625

Combine like terms: -0.25 + 1.5625 = 1.3125
1.5625 + -2.5y + y2 = 1.3125

Factor a perfect square on the left side:
(y + -1.25)(y + -1.25) = 1.3125

Calculate the square root of the right side: 1.145643924

Break this problem into two subproblems by setting 
(y + -1.25) equal to 1.145643924 and -1.145643924.

Subproblem 1
y + -1.25 = 1.145643924

Simplifying
y + -1.25 = 1.145643924

Reorder the terms:
-1.25 + y = 1.145643924

Solving
-1.25 + y = 1.145643924

Solving for variable 'y'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + y = 1.145643924 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + y = 1.145643924 + 1.25
y = 1.145643924 + 1.25

Combine like terms: 1.145643924 + 1.25 = 2.395643924
y = 2.395643924

Simplifying
y = 2.395643924

Subproblem 2
y + -1.25 = -1.145643924

Simplifying
y + -1.25 = -1.145643924

Reorder the terms:
-1.25 + y = -1.145643924

Solving
-1.25 + y = -1.145643924

Solving for variable 'y'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + y = -1.145643924 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + y = -1.145643924 + 1.25
y = -1.145643924 + 1.25

Combine like terms: -1.145643924 + 1.25 = 0.104356076
y = 0.104356076

Simplifying
y = 0.104356076

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.395643924, 0.104356076}