9(c-5)2c=18-4c

Solution for 9(c-5)2c=18-4c equation:

Simplifying
9(c + -5) * 2c = 18 + -4c

Reorder the terms:
9(-5 + c) * 2c = 18 + -4c

Reorder the terms for easier multiplication:
9 * 2c(-5 + c) = 18 + -4c

Multiply 9 * 2
18c(-5 + c) = 18 + -4c
(-5 * 18c + c * 18c) = 18 + -4c
(-90c + 18c2) = 18 + -4c

Solving
-90c + 18c2 = 18 + -4c

Solving for variable 'c'.

Reorder the terms:
-18 + -90c + 4c + 18c2 = 18 + -4c + -18 + 4c

Combine like terms: -90c + 4c = -86c
-18 + -86c + 18c2 = 18 + -4c + -18 + 4c

Reorder the terms:
-18 + -86c + 18c2 = 18 + -18 + -4c + 4c

Combine like terms: 18 + -18 = 0
-18 + -86c + 18c2 = 0 + -4c + 4c
-18 + -86c + 18c2 = -4c + 4c

Combine like terms: -4c + 4c = 0
-18 + -86c + 18c2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + -43c + 9c2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-9 + -43c + 9c2)' equal to zero and attempt to solve:

Simplifying
-9 + -43c + 9c2 = 0

Solving
-9 + -43c + 9c2 = 0

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

Divide each side by '9'.
-1 + -4.777777778c + c2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -4.777777778c + 1 + c2 = 0 + 1

Reorder the terms:
-1 + 1 + -4.777777778c + c2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4.777777778c + c2 = 0 + 1
-4.777777778c + c2 = 0 + 1

Combine like terms: 0 + 1 = 1
-4.777777778c + c2 = 1

The c term is -4.777777778c.  Take half its coefficient (-2.388888889).
Square it (5.706790124) and add it to both sides.

Add '5.706790124' to each side of the equation.
-4.777777778c + 5.706790124 + c2 = 1 + 5.706790124

Reorder the terms:
5.706790124 + -4.777777778c + c2 = 1 + 5.706790124

Combine like terms: 1 + 5.706790124 = 6.706790124
5.706790124 + -4.777777778c + c2 = 6.706790124

Factor a perfect square on the left side:
(c + -2.388888889)(c + -2.388888889) = 6.706790124

Calculate the square root of the right side: 2.589747116

Break this problem into two subproblems by setting 
(c + -2.388888889) equal to 2.589747116 and -2.589747116.

Subproblem 1
c + -2.388888889 = 2.589747116

Simplifying
c + -2.388888889 = 2.589747116

Reorder the terms:
-2.388888889 + c = 2.589747116

Solving
-2.388888889 + c = 2.589747116

Solving for variable 'c'.

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

Add '2.388888889' to each side of the equation.
-2.388888889 + 2.388888889 + c = 2.589747116 + 2.388888889

Combine like terms: -2.388888889 + 2.388888889 = 0.000000000
0.000000000 + c = 2.589747116 + 2.388888889
c = 2.589747116 + 2.388888889

Combine like terms: 2.589747116 + 2.388888889 = 4.978636005
c = 4.978636005

Simplifying
c = 4.978636005

Subproblem 2
c + -2.388888889 = -2.589747116

Simplifying
c + -2.388888889 = -2.589747116

Reorder the terms:
-2.388888889 + c = -2.589747116

Solving
-2.388888889 + c = -2.589747116

Solving for variable 'c'.

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

Add '2.388888889' to each side of the equation.
-2.388888889 + 2.388888889 + c = -2.589747116 + 2.388888889

Combine like terms: -2.388888889 + 2.388888889 = 0.000000000
0.000000000 + c = -2.589747116 + 2.388888889
c = -2.589747116 + 2.388888889

Combine like terms: -2.589747116 + 2.388888889 = -0.200858227
c = -0.200858227

Simplifying
c = -0.200858227

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {4.978636005, -0.200858227}
Solution
c = {4.978636005, -0.200858227}