10(c+9)c=2

Solution for 10(c+9)c=2 equation:

Simplifying
10(c + 9) * c = 2

Reorder the terms:
10(9 + c) * c = 2

Reorder the terms for easier multiplication:
10c(9 + c) = 2
(9 * 10c + c * 10c) = 2
(90c + 10c2) = 2

Solving
90c + 10c2 = 2

Solving for variable 'c'.

Reorder the terms:
-2 + 90c + 10c2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 90c + 10c2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 45c + 5c2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + 45c + 5c2)' equal to zero and attempt to solve:

Simplifying
-1 + 45c + 5c2 = 0

Solving
-1 + 45c + 5c2 = 0

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

Divide each side by '5'.
-0.2 + 9c + c2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + 9c + 0.2 + c2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + 9c + c2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + 9c + c2 = 0 + 0.2
9c + c2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
9c + c2 = 0.2

The c term is 9c.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9c + 20.25 + c2 = 0.2 + 20.25

Reorder the terms:
20.25 + 9c + c2 = 0.2 + 20.25

Combine like terms: 0.2 + 20.25 = 20.45
20.25 + 9c + c2 = 20.45

Factor a perfect square on the left side:
(c + 4.5)(c + 4.5) = 20.45

Calculate the square root of the right side: 4.522167622

Break this problem into two subproblems by setting 
(c + 4.5) equal to 4.522167622 and -4.522167622.

Subproblem 1
c + 4.5 = 4.522167622

Simplifying
c + 4.5 = 4.522167622

Reorder the terms:
4.5 + c = 4.522167622

Solving
4.5 + c = 4.522167622

Solving for variable 'c'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + c = 4.522167622 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + c = 4.522167622 + -4.5
c = 4.522167622 + -4.5

Combine like terms: 4.522167622 + -4.5 = 0.022167622
c = 0.022167622

Simplifying
c = 0.022167622

Subproblem 2
c + 4.5 = -4.522167622

Simplifying
c + 4.5 = -4.522167622

Reorder the terms:
4.5 + c = -4.522167622

Solving
4.5 + c = -4.522167622

Solving for variable 'c'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + c = -4.522167622 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + c = -4.522167622 + -4.5
c = -4.522167622 + -4.5

Combine like terms: -4.522167622 + -4.5 = -9.022167622
c = -9.022167622

Simplifying
c = -9.022167622

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {0.022167622, -9.022167622}
Solution
c = {0.022167622, -9.022167622}