(x+10)(x+1)=90

Solution for (x+10)(x+1)=90 equation:

Simplifying
(x + 10)(x + 1) = 90

Reorder the terms:
(10 + x)(x + 1) = 90

Reorder the terms:
(10 + x)(1 + x) = 90

Multiply (10 + x) * (1 + x)
(10(1 + x) + x(1 + x)) = 90
((1 * 10 + x * 10) + x(1 + x)) = 90
((10 + 10x) + x(1 + x)) = 90
(10 + 10x + (1 * x + x * x)) = 90
(10 + 10x + (1x + x2)) = 90

Combine like terms: 10x + 1x = 11x
(10 + 11x + x2) = 90

Solving
10 + 11x + x2 = 90

Solving for variable 'x'.

Reorder the terms:
10 + -90 + 11x + x2 = 90 + -90

Combine like terms: 10 + -90 = -80
-80 + 11x + x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-80 + 11x + x2 = 0

Factor a trinomial.
(-16 + -1x)(5 + -1x) = 0

Subproblem 1
Set the factor '(-16 + -1x)' equal to zero and attempt to solve:

Simplifying
-16 + -1x = 0

Solving
-16 + -1x = 0

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

Add '16' to each side of the equation.
-16 + 16 + -1x = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1x = 0 + 16
-1x = 0 + 16

Combine like terms: 0 + 16 = 16
-1x = 16

Divide each side by '-1'.
x = -16

Simplifying
x = -16
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-16, 5}