0=a^2+10a+21

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

Simplifying
0 = a2 + 10a + 21

Reorder the terms:
0 = 21 + 10a + a2

Solving
0 = 21 + 10a + a2

Solving for variable 'a'.

Combine like terms: 0 + -21 = -21
-21 + -10a + -1a2 = 21 + 10a + a2 + -21 + -10a + -1a2

Reorder the terms:
-21 + -10a + -1a2 = 21 + -21 + 10a + -10a + a2 + -1a2

Combine like terms: 21 + -21 = 0
-21 + -10a + -1a2 = 0 + 10a + -10a + a2 + -1a2
-21 + -10a + -1a2 = 10a + -10a + a2 + -1a2

Combine like terms: 10a + -10a = 0
-21 + -10a + -1a2 = 0 + a2 + -1a2
-21 + -10a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
-21 + -10a + -1a2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(21 + 10a + a2) = 0

Factor a trinomial.
-1((7 + a)(3 + a)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(7 + a)' equal to zero and attempt to solve:

Simplifying
7 + a = 0

Solving
7 + a = 0

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

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

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

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

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

Simplifying
3 + a = 0

Solving
3 + a = 0

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

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

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

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

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