(x-17)*(x+23)=0

Solution for (x-17)*(x+23)=0 equation:

Simplifying
(x + -17)(x + 23) = 0

Reorder the terms:
(-17 + x)(x + 23) = 0

Reorder the terms:
(-17 + x)(23 + x) = 0

Multiply (-17 + x) * (23 + x)
(-17(23 + x) + x(23 + x)) = 0
((23 * -17 + x * -17) + x(23 + x)) = 0
((-391 + -17x) + x(23 + x)) = 0
(-391 + -17x + (23 * x + x * x)) = 0
(-391 + -17x + (23x + x2)) = 0

Combine like terms: -17x + 23x = 6x
(-391 + 6x + x2) = 0

Solving
-391 + 6x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-23 + -1x)(17 + -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 '(17 + -1x)' equal to zero and attempt to solve:

Simplifying
17 + -1x = 0

Solving
17 + -1x = 0

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

Add '-17' to each side of the equation.
17 + -17 + -1x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -1x = 0 + -17
-1x = 0 + -17

Combine like terms: 0 + -17 = -17
-1x = -17

Divide each side by '-1'.
x = 17

Simplifying
x = 17
Solution
x = {-23, 17}