21+3c-7(2-3c)=4(c-5)3c+27

Solution for 21+3c-7(2-3c)=4(c-5)3c+27 equation:

Simplifying
21 + 3c + -7(2 + -3c) = 4(c + -5) * 3c + 27
21 + 3c + (2 * -7 + -3c * -7) = 4(c + -5) * 3c + 27
21 + 3c + (-14 + 21c) = 4(c + -5) * 3c + 27

Reorder the terms:
21 + -14 + 3c + 21c = 4(c + -5) * 3c + 27

Combine like terms: 21 + -14 = 7
7 + 3c + 21c = 4(c + -5) * 3c + 27

Combine like terms: 3c + 21c = 24c
7 + 24c = 4(c + -5) * 3c + 27

Reorder the terms:
7 + 24c = 4(-5 + c) * 3c + 27

Reorder the terms for easier multiplication:
7 + 24c = 4 * 3c(-5 + c) + 27

Multiply 4 * 3
7 + 24c = 12c(-5 + c) + 27
7 + 24c = (-5 * 12c + c * 12c) + 27
7 + 24c = (-60c + 12c2) + 27

Reorder the terms:
7 + 24c = 27 + -60c + 12c2

Solving
7 + 24c = 27 + -60c + 12c2

Solving for variable 'c'.

Reorder the terms:
7 + -27 + 24c + 60c + -12c2 = 27 + -60c + 12c2 + -27 + 60c + -12c2

Combine like terms: 7 + -27 = -20
-20 + 24c + 60c + -12c2 = 27 + -60c + 12c2 + -27 + 60c + -12c2

Combine like terms: 24c + 60c = 84c
-20 + 84c + -12c2 = 27 + -60c + 12c2 + -27 + 60c + -12c2

Reorder the terms:
-20 + 84c + -12c2 = 27 + -27 + -60c + 60c + 12c2 + -12c2

Combine like terms: 27 + -27 = 0
-20 + 84c + -12c2 = 0 + -60c + 60c + 12c2 + -12c2
-20 + 84c + -12c2 = -60c + 60c + 12c2 + -12c2

Combine like terms: -60c + 60c = 0
-20 + 84c + -12c2 = 0 + 12c2 + -12c2
-20 + 84c + -12c2 = 12c2 + -12c2

Combine like terms: 12c2 + -12c2 = 0
-20 + 84c + -12c2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-5 + 21c + -3c2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-5 + 21c + -3c2)' equal to zero and attempt to solve:

Simplifying
-5 + 21c + -3c2 = 0

Solving
-5 + 21c + -3c2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
1.666666667 + -7c + c2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + -7c + -1.666666667 + c2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + -7c + c2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + -7c + c2 = 0 + -1.666666667
-7c + c2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
-7c + c2 = -1.666666667

The c term is -7c.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7c + 12.25 + c2 = -1.666666667 + 12.25

Reorder the terms:
12.25 + -7c + c2 = -1.666666667 + 12.25

Combine like terms: -1.666666667 + 12.25 = 10.583333333
12.25 + -7c + c2 = 10.583333333

Factor a perfect square on the left side:
(c + -3.5)(c + -3.5) = 10.583333333

Calculate the square root of the right side: 3.253203549

Break this problem into two subproblems by setting 
(c + -3.5) equal to 3.253203549 and -3.253203549.

Subproblem 1
c + -3.5 = 3.253203549

Simplifying
c + -3.5 = 3.253203549

Reorder the terms:
-3.5 + c = 3.253203549

Solving
-3.5 + c = 3.253203549

Solving for variable 'c'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + c = 3.253203549 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + c = 3.253203549 + 3.5
c = 3.253203549 + 3.5

Combine like terms: 3.253203549 + 3.5 = 6.753203549
c = 6.753203549

Simplifying
c = 6.753203549

Subproblem 2
c + -3.5 = -3.253203549

Simplifying
c + -3.5 = -3.253203549

Reorder the terms:
-3.5 + c = -3.253203549

Solving
-3.5 + c = -3.253203549

Solving for variable 'c'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + c = -3.253203549 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + c = -3.253203549 + 3.5
c = -3.253203549 + 3.5

Combine like terms: -3.253203549 + 3.5 = 0.246796451
c = 0.246796451

Simplifying
c = 0.246796451

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {6.753203549, 0.246796451}
Solution
c = {6.753203549, 0.246796451}