6y-4y(y-1)+4=

Solution for 6y-4y(y-1)+4= equation:

Simplifying
6y + -4y(y + -1) + 4 = 0

Reorder the terms:
6y + -4y(-1 + y) + 4 = 0
6y + (-1 * -4y + y * -4y) + 4 = 0
6y + (4y + -4y2) + 4 = 0

Reorder the terms:
4 + 6y + 4y + -4y2 = 0

Combine like terms: 6y + 4y = 10y
4 + 10y + -4y2 = 0

Solving
4 + 10y + -4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + 5y + -2y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(2 + 5y + -2y2)' equal to zero and attempt to solve:

Simplifying
2 + 5y + -2y2 = 0

Solving
2 + 5y + -2y2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-1 + -2.5y + y2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -2.5y + 1 + y2 = 0 + 1

Reorder the terms:
-1 + 1 + -2.5y + y2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2.5y + y2 = 0 + 1
-2.5y + y2 = 0 + 1

Combine like terms: 0 + 1 = 1
-2.5y + y2 = 1

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 = 1 + 1.5625

Reorder the terms:
1.5625 + -2.5y + y2 = 1 + 1.5625

Combine like terms: 1 + 1.5625 = 2.5625
1.5625 + -2.5y + y2 = 2.5625

Factor a perfect square on the left side:
(y + -1.25)(y + -1.25) = 2.5625

Calculate the square root of the right side: 1.600781059

Break this problem into two subproblems by setting 
(y + -1.25) equal to 1.600781059 and -1.600781059.

Subproblem 1
y + -1.25 = 1.600781059

Simplifying
y + -1.25 = 1.600781059

Reorder the terms:
-1.25 + y = 1.600781059

Solving
-1.25 + y = 1.600781059

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 = 1.600781059 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + y = 1.600781059 + 1.25
y = 1.600781059 + 1.25

Combine like terms: 1.600781059 + 1.25 = 2.850781059
y = 2.850781059

Simplifying
y = 2.850781059

Subproblem 2
y + -1.25 = -1.600781059

Simplifying
y + -1.25 = -1.600781059

Reorder the terms:
-1.25 + y = -1.600781059

Solving
-1.25 + y = -1.600781059

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 = -1.600781059 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + y = -1.600781059 + 1.25
y = -1.600781059 + 1.25

Combine like terms: -1.600781059 + 1.25 = -0.350781059
y = -0.350781059

Simplifying
y = -0.350781059

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.850781059, -0.350781059}
Solution
y = {2.850781059, -0.350781059}