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

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

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

Reorder the terms:
(-5 + X)(X + 1) = 0

Reorder the terms:
(-5 + X)(1 + X) = 0

Multiply (-5 + X) * (1 + X)
(-5(1 + X) + X(1 + X)) = 0
((1 * -5 + X * -5) + X(1 + X)) = 0
((-5 + -5X) + X(1 + X)) = 0
(-5 + -5X + (1 * X + X * X)) = 0
(-5 + -5X + (1X + X2)) = 0

Combine like terms: -5X + 1X = -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}