-9(3-c)4c=4

Solution for -9(3-c)4c=4 equation:

Simplifying
-9(3 + -1c) * 4c = 4

Reorder the terms for easier multiplication:
-9 * 4c(3 + -1c) = 4

Multiply -9 * 4
-36c(3 + -1c) = 4
(3 * -36c + -1c * -36c) = 4
(-108c + 36c2) = 4

Solving
-108c + 36c2 = 4

Solving for variable 'c'.

Reorder the terms:
-4 + -108c + 36c2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + -108c + 36c2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + -27c + 9c2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-1 + -27c + 9c2)' equal to zero and attempt to solve:

Simplifying
-1 + -27c + 9c2 = 0

Solving
-1 + -27c + 9c2 = 0

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

Divide each side by '9'.
-0.1111111111 + -3c + c2 = 0

Move the constant term to the right:

Add '0.1111111111' to each side of the equation.
-0.1111111111 + -3c + 0.1111111111 + c2 = 0 + 0.1111111111

Reorder the terms:
-0.1111111111 + 0.1111111111 + -3c + c2 = 0 + 0.1111111111

Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000
0.0000000000 + -3c + c2 = 0 + 0.1111111111
-3c + c2 = 0 + 0.1111111111

Combine like terms: 0 + 0.1111111111 = 0.1111111111
-3c + c2 = 0.1111111111

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 = 0.1111111111 + 2.25

Reorder the terms:
2.25 + -3c + c2 = 0.1111111111 + 2.25

Combine like terms: 0.1111111111 + 2.25 = 2.3611111111
2.25 + -3c + c2 = 2.3611111111

Factor a perfect square on the left side:
(c + -1.5)(c + -1.5) = 2.3611111111

Calculate the square root of the right side: 1.536590743

Break this problem into two subproblems by setting 
(c + -1.5) equal to 1.536590743 and -1.536590743.

Subproblem 1
c + -1.5 = 1.536590743

Simplifying
c + -1.5 = 1.536590743

Reorder the terms:
-1.5 + c = 1.536590743

Solving
-1.5 + c = 1.536590743

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 = 1.536590743 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + c = 1.536590743 + 1.5
c = 1.536590743 + 1.5

Combine like terms: 1.536590743 + 1.5 = 3.036590743
c = 3.036590743

Simplifying
c = 3.036590743

Subproblem 2
c + -1.5 = -1.536590743

Simplifying
c + -1.5 = -1.536590743

Reorder the terms:
-1.5 + c = -1.536590743

Solving
-1.5 + c = -1.536590743

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 = -1.536590743 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + c = -1.536590743 + 1.5
c = -1.536590743 + 1.5

Combine like terms: -1.536590743 + 1.5 = -0.036590743
c = -0.036590743

Simplifying
c = -0.036590743

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {3.036590743, -0.036590743}
Solution
c = {3.036590743, -0.036590743}