x^2+12x+21=10

Solution for x^2+12x+21=10 equation:

Simplifying
x2 + 12x + 21 = 10

Reorder the terms:
21 + 12x + x2 = 10

Solving
21 + 12x + x2 = 10

Solving for variable 'x'.

Reorder the terms:
21 + -10 + 12x + x2 = 10 + -10

Combine like terms: 21 + -10 = 11
11 + 12x + x2 = 10 + -10

Combine like terms: 10 + -10 = 0
11 + 12x + x2 = 0

Factor a trinomial.
(11 + x)(1 + x) = 0

Subproblem 1
Set the factor '(11 + x)' equal to zero and attempt to solve:

Simplifying
11 + x = 0

Solving
11 + x = 0

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

Add '-11' to each side of the equation.
11 + -11 + x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + x = 0 + -11
x = 0 + -11

Combine like terms: 0 + -11 = -11
x = -11

Simplifying
x = -11
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1
Solution
x = {-11, -1}