(x+9)(x-2)=42

Solution for (x+9)(x-2)=42 equation:

Simplifying
(x + 9)(x + -2) = 42

Reorder the terms:
(9 + x)(x + -2) = 42

Reorder the terms:
(9 + x)(-2 + x) = 42

Multiply (9 + x) * (-2 + x)
(9(-2 + x) + x(-2 + x)) = 42
((-2 * 9 + x * 9) + x(-2 + x)) = 42
((-18 + 9x) + x(-2 + x)) = 42
(-18 + 9x + (-2 * x + x * x)) = 42
(-18 + 9x + (-2x + x2)) = 42

Combine like terms: 9x + -2x = 7x
(-18 + 7x + x2) = 42

Solving
-18 + 7x + x2 = 42

Solving for variable 'x'.

Reorder the terms:
-18 + -42 + 7x + x2 = 42 + -42

Combine like terms: -18 + -42 = -60
-60 + 7x + x2 = 42 + -42

Combine like terms: 42 + -42 = 0
-60 + 7x + x2 = 0

Factor a trinomial.
(-12 + -1x)(5 + -1x) = 0

Subproblem 1
Set the factor '(-12 + -1x)' equal to zero and attempt to solve:

Simplifying
-12 + -1x = 0

Solving
-12 + -1x = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1x = 0 + 12
-1x = 0 + 12

Combine like terms: 0 + 12 = 12
-1x = 12

Divide each side by '-1'.
x = -12

Simplifying
x = -12
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 = {-12, 5}