(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.
(-5 + -1x)(23 + -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 '(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
Solution
x = {-5, 23}