(x+5)(x-3)-x=5

Solution for (x+5)(x-3)-x=5 equation:

Simplifying
(x + 5)(x + -3) + -1x = 5

Reorder the terms:
(5 + x)(x + -3) + -1x = 5

Reorder the terms:
(5 + x)(-3 + x) + -1x = 5

Multiply (5 + x) * (-3 + x)
(5(-3 + x) + x(-3 + x)) + -1x = 5
((-3 * 5 + x * 5) + x(-3 + x)) + -1x = 5
((-15 + 5x) + x(-3 + x)) + -1x = 5
(-15 + 5x + (-3 * x + x * x)) + -1x = 5
(-15 + 5x + (-3x + x2)) + -1x = 5

Combine like terms: 5x + -3x = 2x
(-15 + 2x + x2) + -1x = 5

Reorder the terms:
-15 + 2x + -1x + x2 = 5

Combine like terms: 2x + -1x = 1x
-15 + 1x + x2 = 5

Solving
-15 + 1x + x2 = 5

Solving for variable 'x'.

Reorder the terms:
-15 + -5 + 1x + x2 = 5 + -5

Combine like terms: -15 + -5 = -20
-20 + 1x + x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-20 + 1x + x2 = 0

Factor a trinomial.
(-5 + -1x)(4 + -1x) = 0

Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-5, 4}