x(x-5)+(x-5)=0

Solution for x(x-5)+(x-5)=0 equation:

Simplifying
x(x + -5) + (x + -5) = 0

Reorder the terms:
x(-5 + x) + (x + -5) = 0
(-5 * x + x * x) + (x + -5) = 0
(-5x + x2) + (x + -5) = 0

Reorder the terms:
-5x + x2 + (-5 + x) = 0

Remove parenthesis around (-5 + x)
-5x + x2 + -5 + x = 0

Reorder the terms:
-5 + -5x + x + x2 = 0

Combine like terms: -5x + x = -4x
-5 + -4x + x2 = 0

Solving
-5 + -4x + x2 = 0

Solving for variable 'x'.

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

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1
Subproblem 2
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
Solution
x = {-1, 5}