(x+1)(x+42)=0

Solution for (x+1)(x+42)=0 equation:

Simplifying
(x + 1)(x + 42) = 0

Reorder the terms:
(1 + x)(x + 42) = 0

Reorder the terms:
(1 + x)(42 + x) = 0

Multiply (1 + x) * (42 + x)
(1(42 + x) + x(42 + x)) = 0
((42 * 1 + x * 1) + x(42 + x)) = 0
((42 + 1x) + x(42 + x)) = 0
(42 + 1x + (42 * x + x * x)) = 0
(42 + 1x + (42x + x2)) = 0

Combine like terms: 1x + 42x = 43x
(42 + 43x + x2) = 0

Solving
42 + 43x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(42 + x)(1 + x) = 0

Subproblem 1
Set the factor '(42 + x)' equal to zero and attempt to solve:

Simplifying
42 + x = 0

Solving
42 + x = 0

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

Add '-42' to each side of the equation.
42 + -42 + x = 0 + -42

Combine like terms: 42 + -42 = 0
0 + x = 0 + -42
x = 0 + -42

Combine like terms: 0 + -42 = -42
x = -42

Simplifying
x = -42
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {-42, -1}