14c^3-42c^5-49c^4=

Solution for 14c^3-42c^5-49c^4= equation:

Simplifying
14c3 + -42c5 + -49c4 = 0

Reorder the terms:
14c3 + -49c4 + -42c5 = 0

Solving
14c3 + -49c4 + -42c5 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '7c3'.
7c3(2 + -7c + -6c2) = 0

Ignore the factor 7.
Subproblem 1
Set the factor 'c3' equal to zero and attempt to solve:

Simplifying
c3 = 0

Solving
c3 = 0

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

Simplifying
c3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(2 + -7c + -6c2)' equal to zero and attempt to solve:

Simplifying
2 + -7c + -6c2 = 0

Solving
2 + -7c + -6c2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-0.3333333333 + 1.166666667c + c2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + 1.166666667c + 0.3333333333 + c2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + 1.166666667c + c2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + 1.166666667c + c2 = 0 + 0.3333333333
1.166666667c + c2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
1.166666667c + c2 = 0.3333333333

The c term is 1.166666667c.  Take half its coefficient (0.5833333335).
Square it (0.3402777780) and add it to both sides.

Add '0.3402777780' to each side of the equation.
1.166666667c + 0.3402777780 + c2 = 0.3333333333 + 0.3402777780

Reorder the terms:
0.3402777780 + 1.166666667c + c2 = 0.3333333333 + 0.3402777780

Combine like terms: 0.3333333333 + 0.3402777780 = 0.6736111113
0.3402777780 + 1.166666667c + c2 = 0.6736111113

Factor a perfect square on the left side:
(c + 0.5833333335)(c + 0.5833333335) = 0.6736111113

Calculate the square root of the right side: 0.82073815

Break this problem into two subproblems by setting 
(c + 0.5833333335) equal to 0.82073815 and -0.82073815.

Subproblem 1
c + 0.5833333335 = 0.82073815

Simplifying
c + 0.5833333335 = 0.82073815

Reorder the terms:
0.5833333335 + c = 0.82073815

Solving
0.5833333335 + c = 0.82073815

Solving for variable 'c'.

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

Add '-0.5833333335' to each side of the equation.
0.5833333335 + -0.5833333335 + c = 0.82073815 + -0.5833333335

Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000
0.0000000000 + c = 0.82073815 + -0.5833333335
c = 0.82073815 + -0.5833333335

Combine like terms: 0.82073815 + -0.5833333335 = 0.2374048165
c = 0.2374048165

Simplifying
c = 0.2374048165

Subproblem 2
c + 0.5833333335 = -0.82073815

Simplifying
c + 0.5833333335 = -0.82073815

Reorder the terms:
0.5833333335 + c = -0.82073815

Solving
0.5833333335 + c = -0.82073815

Solving for variable 'c'.

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

Add '-0.5833333335' to each side of the equation.
0.5833333335 + -0.5833333335 + c = -0.82073815 + -0.5833333335

Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000
0.0000000000 + c = -0.82073815 + -0.5833333335
c = -0.82073815 + -0.5833333335

Combine like terms: -0.82073815 + -0.5833333335 = -1.4040714835
c = -1.4040714835

Simplifying
c = -1.4040714835

Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {0.2374048165, -1.4040714835}
Solution
c = {0.2374048165, -1.4040714835}