x(x+10)+1=-20

Solution for x(x+10)+1=-20 equation:

Simplifying
x(x + 10) + 1 = -20

Reorder the terms:
x(10 + x) + 1 = -20
(10 * x + x * x) + 1 = -20
(10x + x2) + 1 = -20

Reorder the terms:
1 + 10x + x2 = -20

Solving
1 + 10x + x2 = -20

Solving for variable 'x'.

Reorder the terms:
1 + 20 + 10x + x2 = -20 + 20

Combine like terms: 1 + 20 = 21
21 + 10x + x2 = -20 + 20

Combine like terms: -20 + 20 = 0
21 + 10x + x2 = 0

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

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

Simplifying
7 + x = 0

Solving
7 + x = 0

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

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

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

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

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

Simplifying
3 + x = 0

Solving
3 + x = 0

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

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

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

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

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