(x+1)(x+2)=42

Solution for (x+1)(x+2)=42 equation:

Simplifying
(x + 1)(x + 2) = 42

Reorder the terms:
(1 + x)(x + 2) = 42

Reorder the terms:
(1 + x)(2 + x) = 42

Multiply (1 + x) * (2 + x)
(1(2 + x) + x(2 + x)) = 42
((2 * 1 + x * 1) + x(2 + x)) = 42
((2 + 1x) + x(2 + x)) = 42
(2 + 1x + (2 * x + x * x)) = 42
(2 + 1x + (2x + x2)) = 42

Combine like terms: 1x + 2x = 3x
(2 + 3x + x2) = 42

Solving
2 + 3x + x2 = 42

Solving for variable 'x'.

Reorder the terms:
2 + -42 + 3x + x2 = 42 + -42

Combine like terms: 2 + -42 = -40
-40 + 3x + x2 = 42 + -42

Combine like terms: 42 + -42 = 0
-40 + 3x + x2 = 0

Factor a trinomial.
(-8 + -1x)(5 + -1x) = 0

Subproblem 1
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
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 = {-8, 5}