(1+x)(2+x)=90

Solution for (1+x)(2+x)=90 equation:

Simplifying
(1 + x)(2 + x) = 90

Multiply (1 + x) * (2 + x)
(1(2 + x) + x(2 + x)) = 90
((2 * 1 + x * 1) + x(2 + x)) = 90
((2 + 1x) + x(2 + x)) = 90
(2 + 1x + (2 * x + x * x)) = 90
(2 + 1x + (2x + x2)) = 90

Combine like terms: 1x + 2x = 3x
(2 + 3x + x2) = 90

Solving
2 + 3x + x2 = 90

Solving for variable 'x'.

Reorder the terms:
2 + -90 + 3x + x2 = 90 + -90

Combine like terms: 2 + -90 = -88
-88 + 3x + x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-88 + 3x + x2 = 0

Factor a trinomial.
(-11 + -1x)(8 + -1x) = 0

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

Simplifying
-11 + -1x = 0

Solving
-11 + -1x = 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 + -1x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1x = 0 + 11
-1x = 0 + 11

Combine like terms: 0 + 11 = 11
-1x = 11

Divide each side by '-1'.
x = -11

Simplifying
x = -11
Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-11, 8}