(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.
(-11 + -1x)(6 + -1x) = 0

Subproblem 1
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
Subproblem 2
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
Solution
x = {-11, 6}