(1.8-0.3y)(2y+9)=0

Solution for (1.8-0.3y)(2y+9)=0 equation:

Simplifying
(1.8 + -0.3y)(2y + 9) = 0

Reorder the terms:
(1.8 + -0.3y)(9 + 2y) = 0

Multiply (1.8 + -0.3y) * (9 + 2y)
(1.8(9 + 2y) + -0.3y * (9 + 2y)) = 0
((9 * 1.8 + 2y * 1.8) + -0.3y * (9 + 2y)) = 0
((16.2 + 3.6y) + -0.3y * (9 + 2y)) = 0
(16.2 + 3.6y + (9 * -0.3y + 2y * -0.3y)) = 0
(16.2 + 3.6y + (-2.7y + -0.6y2)) = 0

Combine like terms: 3.6y + -2.7y = 0.9y
(16.2 + 0.9y + -0.6y2) = 0

Solving
16.2 + 0.9y + -0.6y2 = 0

Solving for variable 'y'.

Begin completing the square.  Divide all terms by
-0.6 the coefficient of the squared term: 

Divide each side by '-0.6'.
-27 + -1.5y + y2 = 0

Move the constant term to the right:

Add '27' to each side of the equation.
-27 + -1.5y + 27 + y2 = 0 + 27

Reorder the terms:
-27 + 27 + -1.5y + y2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -1.5y + y2 = 0 + 27
-1.5y + y2 = 0 + 27

Combine like terms: 0 + 27 = 27
-1.5y + y2 = 27

The y term is -1.5y.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5y + 0.5625 + y2 = 27 + 0.5625

Reorder the terms:
0.5625 + -1.5y + y2 = 27 + 0.5625

Combine like terms: 27 + 0.5625 = 27.5625
0.5625 + -1.5y + y2 = 27.5625

Factor a perfect square on the left side:
(y + -0.75)(y + -0.75) = 27.5625

Calculate the square root of the right side: 5.25

Break this problem into two subproblems by setting 
(y + -0.75) equal to 5.25 and -5.25.

Subproblem 1
y + -0.75 = 5.25

Simplifying
y + -0.75 = 5.25

Reorder the terms:
-0.75 + y = 5.25

Solving
-0.75 + y = 5.25

Solving for variable 'y'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + y = 5.25 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + y = 5.25 + 0.75
y = 5.25 + 0.75

Combine like terms: 5.25 + 0.75 = 6
y = 6

Simplifying
y = 6

Subproblem 2
y + -0.75 = -5.25

Simplifying
y + -0.75 = -5.25

Reorder the terms:
-0.75 + y = -5.25

Solving
-0.75 + y = -5.25

Solving for variable 'y'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + y = -5.25 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + y = -5.25 + 0.75
y = -5.25 + 0.75

Combine like terms: -5.25 + 0.75 = -4.5
y = -4.5

Simplifying
y = -4.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {6, -4.5}