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

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

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

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

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

Multiply (-2 + y) * (-3 + y)
(-2(-3 + y) + y(-3 + y)) = -6
((-3 * -2 + y * -2) + y(-3 + y)) = -6
((6 + -2y) + y(-3 + y)) = -6
(6 + -2y + (-3 * y + y * y)) = -6
(6 + -2y + (-3y + y2)) = -6

Combine like terms: -2y + -3y = -5y
(6 + -5y + y2) = -6

Solving
6 + -5y + y2 = -6

Solving for variable 'y'.

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

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

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

Begin completing the square.

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + -5y + -12 + y2 = 0 + -12

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

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

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

The y term is -5y.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5y + 6.25 + y2 = -12 + 6.25

Reorder the terms:
6.25 + -5y + y2 = -12 + 6.25

Combine like terms: -12 + 6.25 = -5.75
6.25 + -5y + y2 = -5.75

Factor a perfect square on the left side:
(y + -2.5)(y + -2.5) = -5.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.