(c^6+7c^5+10c^4)-[c^4(c+2)]=

Solution for (c^6+7c^5+10c^4)-[c^4(c+2)]= equation:

Simplifying
(c6 + 7c5 + 10c4) + -1[c4(c + 2)] = 0

Reorder the terms:
(10c4 + 7c5 + c6) + -1[c4(c + 2)] = 0

Remove parenthesis around (10c4 + 7c5 + c6)
10c4 + 7c5 + c6 + -1[c4(c + 2)] = 0

Reorder the terms:
10c4 + 7c5 + c6 + -1[c4(2 + c)] = 0
10c4 + 7c5 + c6 + -1[(2 * c4 + c * c4)] = 0
10c4 + 7c5 + c6 + -1[(2c4 + c5)] = 0
10c4 + 7c5 + c6 + [2c4 * -1 + c5 * -1] = 0
10c4 + 7c5 + c6 + [-2c4 + -1c5] = 0

Reorder the terms:
10c4 + -2c4 + 7c5 + -1c5 + c6 = 0

Combine like terms: 10c4 + -2c4 = 8c4
8c4 + 7c5 + -1c5 + c6 = 0

Combine like terms: 7c5 + -1c5 = 6c5
8c4 + 6c5 + c6 = 0

Solving
8c4 + 6c5 + c6 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), 'c4'.
c4(8 + 6c + c2) = 0

Factor a trinomial.
c4((4 + c)(2 + c)) = 0

Subproblem 1
Set the factor 'c4' equal to zero and attempt to solve:

Simplifying
c4 = 0

Solving
c4 = 0

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

Simplifying
c4 = 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 '(4 + c)' equal to zero and attempt to solve:

Simplifying
4 + c = 0

Solving
4 + c = 0

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

Add '-4' to each side of the equation.
4 + -4 + c = 0 + -4

Combine like terms: 4 + -4 = 0
0 + c = 0 + -4
c = 0 + -4

Combine like terms: 0 + -4 = -4
c = -4

Simplifying
c = -4
Subproblem 3
Set the factor '(2 + c)' equal to zero and attempt to solve:

Simplifying
2 + c = 0

Solving
2 + c = 0

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

Add '-2' to each side of the equation.
2 + -2 + c = 0 + -2

Combine like terms: 2 + -2 = 0
0 + c = 0 + -2
c = 0 + -2

Combine like terms: 0 + -2 = -2
c = -2

Simplifying
c = -2
Solution
c = {-4, -2}