(-2y+12)(-2y+12)+y^2=6

Solution for (-2y+12)(-2y+12)+y^2=6 equation:

Simplifying
(-2y + 12)(-2y + 12) + y2 = 6

Reorder the terms:
(12 + -2y)(-2y + 12) + y2 = 6

Reorder the terms:
(12 + -2y)(12 + -2y) + y2 = 6

Multiply (12 + -2y) * (12 + -2y)
(12(12 + -2y) + -2y * (12 + -2y)) + y2 = 6
((12 * 12 + -2y * 12) + -2y * (12 + -2y)) + y2 = 6
((144 + -24y) + -2y * (12 + -2y)) + y2 = 6
(144 + -24y + (12 * -2y + -2y * -2y)) + y2 = 6
(144 + -24y + (-24y + 4y2)) + y2 = 6

Combine like terms: -24y + -24y = -48y
(144 + -48y + 4y2) + y2 = 6

Combine like terms: 4y2 + y2 = 5y2
144 + -48y + 5y2 = 6

Solving
144 + -48y + 5y2 = 6

Solving for variable 'y'.

Reorder the terms:
144 + -6 + -48y + 5y2 = 6 + -6

Combine like terms: 144 + -6 = 138
138 + -48y + 5y2 = 6 + -6

Combine like terms: 6 + -6 = 0
138 + -48y + 5y2 = 0

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

Divide each side by '5'.
27.6 + -9.6y + y2 = 0

Move the constant term to the right:

Add '-27.6' to each side of the equation.
27.6 + -9.6y + -27.6 + y2 = 0 + -27.6

Reorder the terms:
27.6 + -27.6 + -9.6y + y2 = 0 + -27.6

Combine like terms: 27.6 + -27.6 = 0.0
0.0 + -9.6y + y2 = 0 + -27.6
-9.6y + y2 = 0 + -27.6

Combine like terms: 0 + -27.6 = -27.6
-9.6y + y2 = -27.6

The y term is -9.6y.  Take half its coefficient (-4.8).
Square it (23.04) and add it to both sides.

Add '23.04' to each side of the equation.
-9.6y + 23.04 + y2 = -27.6 + 23.04

Reorder the terms:
23.04 + -9.6y + y2 = -27.6 + 23.04

Combine like terms: -27.6 + 23.04 = -4.56
23.04 + -9.6y + y2 = -4.56

Factor a perfect square on the left side:
(y + -4.8)(y + -4.8) = -4.56

Can't calculate square root of the right side.

The solution to this equation could not be determined.