(x+9)(x-4)=-42

Solution for (x+9)(x-4)=-42 equation:

Simplifying
(x + 9)(x + -4) = -42

Reorder the terms:
(9 + x)(x + -4) = -42

Reorder the terms:
(9 + x)(-4 + x) = -42

Multiply (9 + x) * (-4 + x)
(9(-4 + x) + x(-4 + x)) = -42
((-4 * 9 + x * 9) + x(-4 + x)) = -42
((-36 + 9x) + x(-4 + x)) = -42
(-36 + 9x + (-4 * x + x * x)) = -42
(-36 + 9x + (-4x + x2)) = -42

Combine like terms: 9x + -4x = 5x
(-36 + 5x + x2) = -42

Solving
-36 + 5x + x2 = -42

Solving for variable 'x'.

Reorder the terms:
-36 + 42 + 5x + x2 = -42 + 42

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

Combine like terms: -42 + 42 = 0
6 + 5x + x2 = 0

Factor a trinomial.
(3 + x)(2 + x) = 0

Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {-3, -2}