2c(c^2+6)=5c^2

Solution for 2c(c^2+6)=5c^2 equation:

Simplifying
2c(c2 + 6) = 5c2

Reorder the terms:
2c(6 + c2) = 5c2
(6 * 2c + c2 * 2c) = 5c2
(12c + 2c3) = 5c2

Solving
12c + 2c3 = 5c2

Solving for variable 'c'.

Reorder the terms:
12c + -5c2 + 2c3 = 5c2 + -5c2

Combine like terms: 5c2 + -5c2 = 0
12c + -5c2 + 2c3 = 0

Factor out the Greatest Common Factor (GCF), 'c'.
c(12 + -5c + 2c2) = 0

Subproblem 1
Set the factor 'c' equal to zero and attempt to solve:

Simplifying
c = 0

Solving
c = 0

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

Simplifying
c = 0
Subproblem 2
Set the factor '(12 + -5c + 2c2)' equal to zero and attempt to solve:

Simplifying
12 + -5c + 2c2 = 0

Solving
12 + -5c + 2c2 = 0

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

Divide each side by '2'.
6 + -2.5c + c2 = 0

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -2.5c + -6 + c2 = 0 + -6

Reorder the terms:
6 + -6 + -2.5c + c2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -2.5c + c2 = 0 + -6
-2.5c + c2 = 0 + -6

Combine like terms: 0 + -6 = -6
-2.5c + c2 = -6

The c term is -2.5c.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5c + 1.5625 + c2 = -6 + 1.5625

Reorder the terms:
1.5625 + -2.5c + c2 = -6 + 1.5625

Combine like terms: -6 + 1.5625 = -4.4375
1.5625 + -2.5c + c2 = -4.4375

Factor a perfect square on the left side:
(c + -1.25)(c + -1.25) = -4.4375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
c = {0}