x(x-1)+5(x-1)=0

Solution for x(x-1)+5(x-1)=0 equation:

Simplifying
x(x + -1) + 5(x + -1) = 0

Reorder the terms:
x(-1 + x) + 5(x + -1) = 0
(-1 * x + x * x) + 5(x + -1) = 0
(-1x + x2) + 5(x + -1) = 0

Reorder the terms:
-1x + x2 + 5(-1 + x) = 0
-1x + x2 + (-1 * 5 + x * 5) = 0
-1x + x2 + (-5 + 5x) = 0

Reorder the terms:
-5 + -1x + 5x + x2 = 0

Combine like terms: -1x + 5x = 4x
-5 + 4x + x2 = 0

Solving
-5 + 4x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5 + -1x)(1 + -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 '(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
Solution
x = {-5, 1}