1(X-6)-(X-2)(X-5)=5

Solution for 1(X-6)-(X-2)(X-5)=5 equation:

Simplifying
1(X + -6) + -1(X + -2)(X + -5) = 5

Reorder the terms:
1(-6 + X) + -1(X + -2)(X + -5) = 5
(-6 * 1 + X * 1) + -1(X + -2)(X + -5) = 5
(-6 + 1X) + -1(X + -2)(X + -5) = 5

Reorder the terms:
-6 + 1X + -1(-2 + X)(X + -5) = 5

Reorder the terms:
-6 + 1X + -1(-2 + X)(-5 + X) = 5

Multiply (-2 + X) * (-5 + X)
-6 + 1X + -1(-2(-5 + X) + X(-5 + X)) = 5
-6 + 1X + -1((-5 * -2 + X * -2) + X(-5 + X)) = 5
-6 + 1X + -1((10 + -2X) + X(-5 + X)) = 5
-6 + 1X + -1(10 + -2X + (-5 * X + X * X)) = 5
-6 + 1X + -1(10 + -2X + (-5X + X2)) = 5

Combine like terms: -2X + -5X = -7X
-6 + 1X + -1(10 + -7X + X2) = 5
-6 + 1X + (10 * -1 + -7X * -1 + X2 * -1) = 5
-6 + 1X + (-10 + 7X + -1X2) = 5

Reorder the terms:
-6 + -10 + 1X + 7X + -1X2 = 5

Combine like terms: -6 + -10 = -16
-16 + 1X + 7X + -1X2 = 5

Combine like terms: 1X + 7X = 8X
-16 + 8X + -1X2 = 5

Solving
-16 + 8X + -1X2 = 5

Solving for variable 'X'.

Reorder the terms:
-16 + -5 + 8X + -1X2 = 5 + -5

Combine like terms: -16 + -5 = -21
-21 + 8X + -1X2 = 5 + -5

Combine like terms: 5 + -5 = 0
-21 + 8X + -1X2 = 0

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

Divide each side by '-1'.
21 + -8X + X2 = 0

Move the constant term to the right:

Add '-21' to each side of the equation.
21 + -8X + -21 + X2 = 0 + -21

Reorder the terms:
21 + -21 + -8X + X2 = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -8X + X2 = 0 + -21
-8X + X2 = 0 + -21

Combine like terms: 0 + -21 = -21
-8X + X2 = -21

The X term is -8X.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8X + 16 + X2 = -21 + 16

Reorder the terms:
16 + -8X + X2 = -21 + 16

Combine like terms: -21 + 16 = -5
16 + -8X + X2 = -5

Factor a perfect square on the left side:
(X + -4)(X + -4) = -5

Can't calculate square root of the right side.

The solution to this equation could not be determined.