(x+6)(x-5)=42

Solution for (x+6)(x-5)=42 equation:

Simplifying
(x + 6)(x + -5) = 42

Reorder the terms:
(6 + x)(x + -5) = 42

Reorder the terms:
(6 + x)(-5 + x) = 42

Multiply (6 + x) * (-5 + x)
(6(-5 + x) + x(-5 + x)) = 42
((-5 * 6 + x * 6) + x(-5 + x)) = 42
((-30 + 6x) + x(-5 + x)) = 42
(-30 + 6x + (-5 * x + x * x)) = 42
(-30 + 6x + (-5x + x2)) = 42

Combine like terms: 6x + -5x = 1x
(-30 + 1x + x2) = 42

Solving
-30 + 1x + x2 = 42

Solving for variable 'x'.

Reorder the terms:
-30 + -42 + 1x + x2 = 42 + -42

Combine like terms: -30 + -42 = -72
-72 + 1x + x2 = 42 + -42

Combine like terms: 42 + -42 = 0
-72 + 1x + x2 = 0

Factor a trinomial.
(-9 + -1x)(8 + -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 '(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
Solution
x = {-9, 8}