c+17=(c-3)(c-2)

Solution for c+17=(c-3)(c-2) equation:

Simplifying
c + 17 = (c + -3)(c + -2)

Reorder the terms:
17 + c = (c + -3)(c + -2)

Reorder the terms:
17 + c = (-3 + c)(c + -2)

Reorder the terms:
17 + c = (-3 + c)(-2 + c)

Multiply (-3 + c) * (-2 + c)
17 + c = (-3(-2 + c) + c(-2 + c))
17 + c = ((-2 * -3 + c * -3) + c(-2 + c))
17 + c = ((6 + -3c) + c(-2 + c))
17 + c = (6 + -3c + (-2 * c + c * c))
17 + c = (6 + -3c + (-2c + c2))

Combine like terms: -3c + -2c = -5c
17 + c = (6 + -5c + c2)

Solving
17 + c = 6 + -5c + c2

Solving for variable 'c'.

Reorder the terms:
17 + -6 + c + 5c + -1c2 = 6 + -5c + c2 + -6 + 5c + -1c2

Combine like terms: 17 + -6 = 11
11 + c + 5c + -1c2 = 6 + -5c + c2 + -6 + 5c + -1c2

Combine like terms: c + 5c = 6c
11 + 6c + -1c2 = 6 + -5c + c2 + -6 + 5c + -1c2

Reorder the terms:
11 + 6c + -1c2 = 6 + -6 + -5c + 5c + c2 + -1c2

Combine like terms: 6 + -6 = 0
11 + 6c + -1c2 = 0 + -5c + 5c + c2 + -1c2
11 + 6c + -1c2 = -5c + 5c + c2 + -1c2

Combine like terms: -5c + 5c = 0
11 + 6c + -1c2 = 0 + c2 + -1c2
11 + 6c + -1c2 = c2 + -1c2

Combine like terms: c2 + -1c2 = 0
11 + 6c + -1c2 = 0

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

Divide each side by '-1'.
-11 + -6c + c2 = 0

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + -6c + 11 + c2 = 0 + 11

Reorder the terms:
-11 + 11 + -6c + c2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -6c + c2 = 0 + 11
-6c + c2 = 0 + 11

Combine like terms: 0 + 11 = 11
-6c + c2 = 11

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

Add '9' to each side of the equation.
-6c + 9 + c2 = 11 + 9

Reorder the terms:
9 + -6c + c2 = 11 + 9

Combine like terms: 11 + 9 = 20
9 + -6c + c2 = 20

Factor a perfect square on the left side:
(c + -3)(c + -3) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(c + -3) equal to 4.472135955 and -4.472135955.

Subproblem 1
c + -3 = 4.472135955

Simplifying
c + -3 = 4.472135955

Reorder the terms:
-3 + c = 4.472135955

Solving
-3 + c = 4.472135955

Solving for variable 'c'.

Move all terms containing c to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + c = 4.472135955 + 3

Combine like terms: -3 + 3 = 0
0 + c = 4.472135955 + 3
c = 4.472135955 + 3

Combine like terms: 4.472135955 + 3 = 7.472135955
c = 7.472135955

Simplifying
c = 7.472135955

Subproblem 2
c + -3 = -4.472135955

Simplifying
c + -3 = -4.472135955

Reorder the terms:
-3 + c = -4.472135955

Solving
-3 + c = -4.472135955

Solving for variable 'c'.

Move all terms containing c to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + c = -4.472135955 + 3

Combine like terms: -3 + 3 = 0
0 + c = -4.472135955 + 3
c = -4.472135955 + 3

Combine like terms: -4.472135955 + 3 = -1.472135955
c = -1.472135955

Simplifying
c = -1.472135955

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {7.472135955, -1.472135955}