(x+3)(x+2)=42

Solution for (x+3)(x+2)=42 equation:

Simplifying
(x + 3)(x + 2) = 42

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

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

Multiply (3 + x) * (2 + x)
(3(2 + x) + x(2 + x)) = 42
((2 * 3 + x * 3) + x(2 + x)) = 42
((6 + 3x) + x(2 + x)) = 42
(6 + 3x + (2 * x + x * x)) = 42
(6 + 3x + (2x + x2)) = 42

Combine like terms: 3x + 2x = 5x
(6 + 5x + x2) = 42

Solving
6 + 5x + x2 = 42

Solving for variable 'x'.

Reorder the terms:
6 + -42 + 5x + x2 = 42 + -42

Combine like terms: 6 + -42 = -36
-36 + 5x + x2 = 42 + -42

Combine like terms: 42 + -42 = 0
-36 + 5x + x2 = 0

Factor a trinomial.
(-9 + -1x)(4 + -1x) = 0

Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-9, 4}