3c(4c+6)-18=168

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Solution for 3c(4c+6)-18=168 equation: 


Simplifying
3c(4c + 6) + -18 = 168

Reorder the terms:
3c(6 + 4c) + -18 = 168
(6 * 3c + 4c * 3c) + -18 = 168
(18c + 12c2) + -18 = 168

Reorder the terms:
-18 + 18c + 12c2 = 168

Solving
-18 + 18c + 12c2 = 168

Solving for variable 'c'.

Reorder the terms:
-18 + -168 + 18c + 12c2 = 168 + -168

Combine like terms: -18 + -168 = -186
-186 + 18c + 12c2 = 168 + -168

Combine like terms: 168 + -168 = 0
-186 + 18c + 12c2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-31 + 3c + 2c2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-31 + 3c + 2c2)' equal to zero and attempt to solve:

Simplifying
-31 + 3c + 2c2 = 0

Solving
-31 + 3c + 2c2 = 0

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

Divide each side by '2'.
-15.5 + 1.5c + c2 = 0

Move the constant term to the right:

Add '15.5' to each side of the equation.
-15.5 + 1.5c + 15.5 + c2 = 0 + 15.5

Reorder the terms:
-15.5 + 15.5 + 1.5c + c2 = 0 + 15.5

Combine like terms: -15.5 + 15.5 = 0.0
0.0 + 1.5c + c2 = 0 + 15.5
1.5c + c2 = 0 + 15.5

Combine like terms: 0 + 15.5 = 15.5
1.5c + c2 = 15.5

The c term is 1.5c.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5c + 0.5625 + c2 = 15.5 + 0.5625

Reorder the terms:
0.5625 + 1.5c + c2 = 15.5 + 0.5625

Combine like terms: 15.5 + 0.5625 = 16.0625
0.5625 + 1.5c + c2 = 16.0625

Factor a perfect square on the left side:
(c + 0.75)(c + 0.75) = 16.0625

Calculate the square root of the right side: 4.007804885

Break this problem into two subproblems by setting 
(c + 0.75) equal to 4.007804885 and -4.007804885.


Subproblem 1
c + 0.75 = 4.007804885

Simplifying
c + 0.75 = 4.007804885

Reorder the terms:
0.75 + c = 4.007804885

Solving
0.75 + c = 4.007804885

Solving for variable 'c'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + c = 4.007804885 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + c = 4.007804885 + -0.75
c = 4.007804885 + -0.75

Combine like terms: 4.007804885 + -0.75 = 3.257804885
c = 3.257804885

Simplifying
c = 3.257804885


Subproblem 2
c + 0.75 = -4.007804885

Simplifying
c + 0.75 = -4.007804885

Reorder the terms:
0.75 + c = -4.007804885

Solving
0.75 + c = -4.007804885

Solving for variable 'c'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + c = -4.007804885 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + c = -4.007804885 + -0.75
c = -4.007804885 + -0.75

Combine like terms: -4.007804885 + -0.75 = -4.757804885
c = -4.757804885

Simplifying
c = -4.757804885


Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {3.257804885, -4.757804885}
Solution
c = {3.257804885, -4.757804885}

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