(x+2)(x-5)=8

Solution for (x+2)(x-5)=8 equation:

Simplifying
(x + 2)(x + -5) = 8

Reorder the terms:
(2 + x)(x + -5) = 8

Reorder the terms:
(2 + x)(-5 + x) = 8

Multiply (2 + x) * (-5 + x)
(2(-5 + x) + x(-5 + x)) = 8
((-5 * 2 + x * 2) + x(-5 + x)) = 8
((-10 + 2x) + x(-5 + x)) = 8
(-10 + 2x + (-5 * x + x * x)) = 8
(-10 + 2x + (-5x + x2)) = 8

Combine like terms: 2x + -5x = -3x
(-10 + -3x + x2) = 8

Solving
-10 + -3x + x2 = 8

Solving for variable 'x'.

Reorder the terms:
-10 + -8 + -3x + x2 = 8 + -8

Combine like terms: -10 + -8 = -18
-18 + -3x + x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-18 + -3x + x2 = 0

Factor a trinomial.
(-3 + -1x)(6 + -1x) = 0

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

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 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 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3
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 = {-3, 6}