(x+3)(x-8)=42

Solution for (x+3)(x-8)=42 equation:

Simplifying
(x + 3)(x + -8) = 42

Reorder the terms:
(3 + x)(x + -8) = 42

Reorder the terms:
(3 + x)(-8 + x) = 42

Multiply (3 + x) * (-8 + x)
(3(-8 + x) + x(-8 + x)) = 42
((-8 * 3 + x * 3) + x(-8 + x)) = 42
((-24 + 3x) + x(-8 + x)) = 42
(-24 + 3x + (-8 * x + x * x)) = 42
(-24 + 3x + (-8x + x2)) = 42

Combine like terms: 3x + -8x = -5x
(-24 + -5x + x2) = 42

Solving
-24 + -5x + x2 = 42

Solving for variable 'x'.

Reorder the terms:
-24 + -42 + -5x + x2 = 42 + -42

Combine like terms: -24 + -42 = -66
-66 + -5x + x2 = 42 + -42

Combine like terms: 42 + -42 = 0
-66 + -5x + x2 = 0

Factor a trinomial.
(-6 + -1x)(11 + -1x) = 0

Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {-6, 11}