9(c-3)c=8

Solution for 9(c-3)c=8 equation:

Simplifying
9(c + -3) * c = 8

Reorder the terms:
9(-3 + c) * c = 8

Reorder the terms for easier multiplication:
9c(-3 + c) = 8
(-3 * 9c + c * 9c) = 8
(-27c + 9c2) = 8

Solving
-27c + 9c2 = 8

Solving for variable 'c'.

Reorder the terms:
-8 + -27c + 9c2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + -27c + 9c2 = 0

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

Divide each side by '9'.
-0.8888888889 + -3c + c2 = 0

Move the constant term to the right:

Add '0.8888888889' to each side of the equation.
-0.8888888889 + -3c + 0.8888888889 + c2 = 0 + 0.8888888889

Reorder the terms:
-0.8888888889 + 0.8888888889 + -3c + c2 = 0 + 0.8888888889

Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000
0.0000000000 + -3c + c2 = 0 + 0.8888888889
-3c + c2 = 0 + 0.8888888889

Combine like terms: 0 + 0.8888888889 = 0.8888888889
-3c + c2 = 0.8888888889

The c term is -3c.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3c + 2.25 + c2 = 0.8888888889 + 2.25

Reorder the terms:
2.25 + -3c + c2 = 0.8888888889 + 2.25

Combine like terms: 0.8888888889 + 2.25 = 3.1388888889
2.25 + -3c + c2 = 3.1388888889

Factor a perfect square on the left side:
(c + -1.5)(c + -1.5) = 3.1388888889

Calculate the square root of the right side: 1.771690969

Break this problem into two subproblems by setting 
(c + -1.5) equal to 1.771690969 and -1.771690969.

Subproblem 1
c + -1.5 = 1.771690969

Simplifying
c + -1.5 = 1.771690969

Reorder the terms:
-1.5 + c = 1.771690969

Solving
-1.5 + c = 1.771690969

Solving for variable 'c'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + c = 1.771690969 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + c = 1.771690969 + 1.5
c = 1.771690969 + 1.5

Combine like terms: 1.771690969 + 1.5 = 3.271690969
c = 3.271690969

Simplifying
c = 3.271690969

Subproblem 2
c + -1.5 = -1.771690969

Simplifying
c + -1.5 = -1.771690969

Reorder the terms:
-1.5 + c = -1.771690969

Solving
-1.5 + c = -1.771690969

Solving for variable 'c'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + c = -1.771690969 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + c = -1.771690969 + 1.5
c = -1.771690969 + 1.5

Combine like terms: -1.771690969 + 1.5 = -0.271690969
c = -0.271690969

Simplifying
c = -0.271690969

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {3.271690969, -0.271690969}