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

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

Simplifying
y(2 + -1y) = 6 + -1(y + 3y + -4)
(2 * y + -1y * y) = 6 + -1(y + 3y + -4)
(2y + -1y2) = 6 + -1(y + 3y + -4)

Reorder the terms:
2y + -1y2 = 6 + -1(-4 + y + 3y)

Combine like terms: y + 3y = 4y
2y + -1y2 = 6 + -1(-4 + 4y)
2y + -1y2 = 6 + (-4 * -1 + 4y * -1)
2y + -1y2 = 6 + (4 + -4y)

Combine like terms: 6 + 4 = 10
2y + -1y2 = 10 + -4y

Solving
2y + -1y2 = 10 + -4y

Solving for variable 'y'.

Reorder the terms:
-10 + 2y + 4y + -1y2 = 10 + -4y + -10 + 4y

Combine like terms: 2y + 4y = 6y
-10 + 6y + -1y2 = 10 + -4y + -10 + 4y

Reorder the terms:
-10 + 6y + -1y2 = 10 + -10 + -4y + 4y

Combine like terms: 10 + -10 = 0
-10 + 6y + -1y2 = 0 + -4y + 4y
-10 + 6y + -1y2 = -4y + 4y

Combine like terms: -4y + 4y = 0
-10 + 6y + -1y2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
10 + -6y + y2 = 0

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -6y + -10 + y2 = 0 + -10

Reorder the terms:
10 + -10 + -6y + y2 = 0 + -10

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

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

The y term is -6y.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6y + 9 + y2 = -10 + 9

Reorder the terms:
9 + -6y + y2 = -10 + 9

Combine like terms: -10 + 9 = -1
9 + -6y + y2 = -1

Factor a perfect square on the left side:
(y + -3)(y + -3) = -1

Can't calculate square root of the right side.

The solution to this equation could not be determined.