(x+1)(x+10)=22

Solution for (x+1)(x+10)=22 equation:

Simplifying
(x + 1)(x + 10) = 22

Reorder the terms:
(1 + x)(x + 10) = 22

Reorder the terms:
(1 + x)(10 + x) = 22

Multiply (1 + x) * (10 + x)
(1(10 + x) + x(10 + x)) = 22
((10 * 1 + x * 1) + x(10 + x)) = 22
((10 + 1x) + x(10 + x)) = 22
(10 + 1x + (10 * x + x * x)) = 22
(10 + 1x + (10x + x2)) = 22

Combine like terms: 1x + 10x = 11x
(10 + 11x + x2) = 22

Solving
10 + 11x + x2 = 22

Solving for variable 'x'.

Reorder the terms:
10 + -22 + 11x + x2 = 22 + -22

Combine like terms: 10 + -22 = -12
-12 + 11x + x2 = 22 + -22

Combine like terms: 22 + -22 = 0
-12 + 11x + x2 = 0

Factor a trinomial.
(-12 + -1x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-12 + -1x)' equal to zero and attempt to solve:

Simplifying
-12 + -1x = 0

Solving
-12 + -1x = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1x = 0 + 12
-1x = 0 + 12

Combine like terms: 0 + 12 = 12
-1x = 12

Divide each side by '-1'.
x = -12

Simplifying
x = -12
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {-12, 1}