6y-3y(2y-4)-5=

Solution for 6y-3y(2y-4)-5= equation:

Simplifying
6y + -3y(2y + -4) + -5 = 0

Reorder the terms:
6y + -3y(-4 + 2y) + -5 = 0
6y + (-4 * -3y + 2y * -3y) + -5 = 0
6y + (12y + -6y2) + -5 = 0

Reorder the terms:
-5 + 6y + 12y + -6y2 = 0

Combine like terms: 6y + 12y = 18y
-5 + 18y + -6y2 = 0

Solving
-5 + 18y + -6y2 = 0

Solving for variable 'y'.

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
0.8333333333 + -3y + y2 = 0

Move the constant term to the right:

Add '-0.8333333333' to each side of the equation.
0.8333333333 + -3y + -0.8333333333 + y2 = 0 + -0.8333333333

Reorder the terms:
0.8333333333 + -0.8333333333 + -3y + y2 = 0 + -0.8333333333

Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000
0.0000000000 + -3y + y2 = 0 + -0.8333333333
-3y + y2 = 0 + -0.8333333333

Combine like terms: 0 + -0.8333333333 = -0.8333333333
-3y + y2 = -0.8333333333

The y term is -3y.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3y + 2.25 + y2 = -0.8333333333 + 2.25

Reorder the terms:
2.25 + -3y + y2 = -0.8333333333 + 2.25

Combine like terms: -0.8333333333 + 2.25 = 1.4166666667
2.25 + -3y + y2 = 1.4166666667

Factor a perfect square on the left side:
(y + -1.5)(y + -1.5) = 1.4166666667

Calculate the square root of the right side: 1.190238071

Break this problem into two subproblems by setting 
(y + -1.5) equal to 1.190238071 and -1.190238071.

Subproblem 1
y + -1.5 = 1.190238071

Simplifying
y + -1.5 = 1.190238071

Reorder the terms:
-1.5 + y = 1.190238071

Solving
-1.5 + y = 1.190238071

Solving for variable 'y'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + y = 1.190238071 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = 1.190238071 + 1.5
y = 1.190238071 + 1.5

Combine like terms: 1.190238071 + 1.5 = 2.690238071
y = 2.690238071

Simplifying
y = 2.690238071

Subproblem 2
y + -1.5 = -1.190238071

Simplifying
y + -1.5 = -1.190238071

Reorder the terms:
-1.5 + y = -1.190238071

Solving
-1.5 + y = -1.190238071

Solving for variable 'y'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + y = -1.190238071 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = -1.190238071 + 1.5
y = -1.190238071 + 1.5

Combine like terms: -1.190238071 + 1.5 = 0.309761929
y = 0.309761929

Simplifying
y = 0.309761929

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.690238071, 0.309761929}