(X-5)(X+23)=0

Solution for (X-5)(X+23)=0 equation:

Simplifying
(X + -5)(X + 23) = 0

Reorder the terms:
(-5 + X)(X + 23) = 0

Reorder the terms:
(-5 + X)(23 + X) = 0

Multiply (-5 + X) * (23 + X)
(-5(23 + X) + X(23 + X)) = 0
((23 * -5 + X * -5) + X(23 + X)) = 0
((-115 + -5X) + X(23 + X)) = 0
(-115 + -5X + (23 * X + X * X)) = 0
(-115 + -5X + (23X + X2)) = 0

Combine like terms: -5X + 23X = 18X
(-115 + 18X + X2) = 0

Solving
-115 + 18X + X2 = 0

Solving for variable 'X'.

Factor a trinomial.
(-23 + -1X)(5 + -1X) = 0

Subproblem 1
Set the factor '(-23 + -1X)' equal to zero and attempt to solve:

Simplifying
-23 + -1X = 0

Solving
-23 + -1X = 0

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

Add '23' to each side of the equation.
-23 + 23 + -1X = 0 + 23

Combine like terms: -23 + 23 = 0
0 + -1X = 0 + 23
-1X = 0 + 23

Combine like terms: 0 + 23 = 23
-1X = 23

Divide each side by '-1'.
X = -23

Simplifying
X = -23
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 = {-23, 5}