3(2y^2-9y+5)-9(3-2y^2)=

Solution for 3(2y^2-9y+5)-9(3-2y^2)= equation:

Simplifying
3(2y2 + -9y + 5) + -9(3 + -2y2) = 0

Reorder the terms:
3(5 + -9y + 2y2) + -9(3 + -2y2) = 0
(5 * 3 + -9y * 3 + 2y2 * 3) + -9(3 + -2y2) = 0
(15 + -27y + 6y2) + -9(3 + -2y2) = 0
15 + -27y + 6y2 + (3 * -9 + -2y2 * -9) = 0
15 + -27y + 6y2 + (-27 + 18y2) = 0

Reorder the terms:
15 + -27 + -27y + 6y2 + 18y2 = 0

Combine like terms: 15 + -27 = -12
-12 + -27y + 6y2 + 18y2 = 0

Combine like terms: 6y2 + 18y2 = 24y2
-12 + -27y + 24y2 = 0

Solving
-12 + -27y + 24y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + -9y + 8y2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-4 + -9y + 8y2)' equal to zero and attempt to solve:

Simplifying
-4 + -9y + 8y2 = 0

Solving
-4 + -9y + 8y2 = 0

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

Divide each side by '8'.
-0.5 + -1.125y + y2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -1.125y + 0.5 + y2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -1.125y + y2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -1.125y + y2 = 0 + 0.5
-1.125y + y2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-1.125y + y2 = 0.5

The y term is -1.125y.  Take half its coefficient (-0.5625).
Square it (0.31640625) and add it to both sides.

Add '0.31640625' to each side of the equation.
-1.125y + 0.31640625 + y2 = 0.5 + 0.31640625

Reorder the terms:
0.31640625 + -1.125y + y2 = 0.5 + 0.31640625

Combine like terms: 0.5 + 0.31640625 = 0.81640625
0.31640625 + -1.125y + y2 = 0.81640625

Factor a perfect square on the left side:
(y + -0.5625)(y + -0.5625) = 0.81640625

Calculate the square root of the right side: 0.903552018

Break this problem into two subproblems by setting 
(y + -0.5625) equal to 0.903552018 and -0.903552018.

Subproblem 1
y + -0.5625 = 0.903552018

Simplifying
y + -0.5625 = 0.903552018

Reorder the terms:
-0.5625 + y = 0.903552018

Solving
-0.5625 + y = 0.903552018

Solving for variable 'y'.

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

Add '0.5625' to each side of the equation.
-0.5625 + 0.5625 + y = 0.903552018 + 0.5625

Combine like terms: -0.5625 + 0.5625 = 0.0000
0.0000 + y = 0.903552018 + 0.5625
y = 0.903552018 + 0.5625

Combine like terms: 0.903552018 + 0.5625 = 1.466052018
y = 1.466052018

Simplifying
y = 1.466052018

Subproblem 2
y + -0.5625 = -0.903552018

Simplifying
y + -0.5625 = -0.903552018

Reorder the terms:
-0.5625 + y = -0.903552018

Solving
-0.5625 + y = -0.903552018

Solving for variable 'y'.

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

Add '0.5625' to each side of the equation.
-0.5625 + 0.5625 + y = -0.903552018 + 0.5625

Combine like terms: -0.5625 + 0.5625 = 0.0000
0.0000 + y = -0.903552018 + 0.5625
y = -0.903552018 + 0.5625

Combine like terms: -0.903552018 + 0.5625 = -0.341052018
y = -0.341052018

Simplifying
y = -0.341052018

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.466052018, -0.341052018}
Solution
y = {1.466052018, -0.341052018}