c^2+10c+21=0

Solution for c^2+10c+21=0 equation:

Simplifying
c2 + 10c + 21 = 0

Reorder the terms:
21 + 10c + c2 = 0

Solving
21 + 10c + c2 = 0

Solving for variable 'c'.

Factor a trinomial.
(7 + c)(3 + c) = 0

Subproblem 1
Set the factor '(7 + c)' equal to zero and attempt to solve:

Simplifying
7 + c = 0

Solving
7 + c = 0

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

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

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

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

Simplifying
c = -7
Subproblem 2
Set the factor '(3 + c)' equal to zero and attempt to solve:

Simplifying
3 + c = 0

Solving
3 + c = 0

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

Add '-3' to each side of the equation.
3 + -3 + c = 0 + -3

Combine like terms: 3 + -3 = 0
0 + c = 0 + -3
c = 0 + -3

Combine like terms: 0 + -3 = -3
c = -3

Simplifying
c = -3
Solution
c = {-7, -3}