-5y(2y-3)=4(1-3y)+12

Solution for -5y(2y-3)=4(1-3y)+12 equation:

Simplifying
-5y(2y + -3) = 4(1 + -3y) + 12

Reorder the terms:
-5y(-3 + 2y) = 4(1 + -3y) + 12
(-3 * -5y + 2y * -5y) = 4(1 + -3y) + 12
(15y + -10y2) = 4(1 + -3y) + 12
15y + -10y2 = (1 * 4 + -3y * 4) + 12
15y + -10y2 = (4 + -12y) + 12

Reorder the terms:
15y + -10y2 = 4 + 12 + -12y

Combine like terms: 4 + 12 = 16
15y + -10y2 = 16 + -12y

Solving
15y + -10y2 = 16 + -12y

Solving for variable 'y'.

Reorder the terms:
-16 + 15y + 12y + -10y2 = 16 + -12y + -16 + 12y

Combine like terms: 15y + 12y = 27y
-16 + 27y + -10y2 = 16 + -12y + -16 + 12y

Reorder the terms:
-16 + 27y + -10y2 = 16 + -16 + -12y + 12y

Combine like terms: 16 + -16 = 0
-16 + 27y + -10y2 = 0 + -12y + 12y
-16 + 27y + -10y2 = -12y + 12y

Combine like terms: -12y + 12y = 0
-16 + 27y + -10y2 = 0

Begin completing the square.  Divide all terms by
-10 the coefficient of the squared term: 

Divide each side by '-10'.
1.6 + -2.7y + y2 = 0.0

Move the constant term to the right:

Add '-1.6' to each side of the equation.
1.6 + -2.7y + -1.6 + y2 = 0.0 + -1.6

Reorder the terms:
1.6 + -1.6 + -2.7y + y2 = 0.0 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + -2.7y + y2 = 0.0 + -1.6
-2.7y + y2 = 0.0 + -1.6

Combine like terms: 0.0 + -1.6 = -1.6
-2.7y + y2 = -1.6

The y term is -2.7y.  Take half its coefficient (-1.35).
Square it (1.8225) and add it to both sides.

Add '1.8225' to each side of the equation.
-2.7y + 1.8225 + y2 = -1.6 + 1.8225

Reorder the terms:
1.8225 + -2.7y + y2 = -1.6 + 1.8225

Combine like terms: -1.6 + 1.8225 = 0.2225
1.8225 + -2.7y + y2 = 0.2225

Factor a perfect square on the left side:
(y + -1.35)(y + -1.35) = 0.2225

Calculate the square root of the right side: 0.471699057

Break this problem into two subproblems by setting 
(y + -1.35) equal to 0.471699057 and -0.471699057.

Subproblem 1
y + -1.35 = 0.471699057

Simplifying
y + -1.35 = 0.471699057

Reorder the terms:
-1.35 + y = 0.471699057

Solving
-1.35 + y = 0.471699057

Solving for variable 'y'.

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

Add '1.35' to each side of the equation.
-1.35 + 1.35 + y = 0.471699057 + 1.35

Combine like terms: -1.35 + 1.35 = 0.00
0.00 + y = 0.471699057 + 1.35
y = 0.471699057 + 1.35

Combine like terms: 0.471699057 + 1.35 = 1.821699057
y = 1.821699057

Simplifying
y = 1.821699057

Subproblem 2
y + -1.35 = -0.471699057

Simplifying
y + -1.35 = -0.471699057

Reorder the terms:
-1.35 + y = -0.471699057

Solving
-1.35 + y = -0.471699057

Solving for variable 'y'.

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

Add '1.35' to each side of the equation.
-1.35 + 1.35 + y = -0.471699057 + 1.35

Combine like terms: -1.35 + 1.35 = 0.00
0.00 + y = -0.471699057 + 1.35
y = -0.471699057 + 1.35

Combine like terms: -0.471699057 + 1.35 = 0.878300943
y = 0.878300943

Simplifying
y = 0.878300943

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.821699057, 0.878300943}