(x-5)(x+3)=0

Solution for (x-5)(x+3)=0 equation:

Simplifying
(x + -5)(x + 3) = 0

Reorder the terms:
(-5 + x)(x + 3) = 0

Reorder the terms:
(-5 + x)(3 + x) = 0

Multiply (-5 + x) * (3 + x)
(-5(3 + x) + x(3 + x)) = 0
((3 * -5 + x * -5) + x(3 + x)) = 0
((-15 + -5x) + x(3 + x)) = 0
(-15 + -5x + (3 * x + x * x)) = 0
(-15 + -5x + (3x + x2)) = 0

Combine like terms: -5x + 3x = -2x
(-15 + -2x + x2) = 0

Solving
-15 + -2x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-3 + -1x)(5 + -1x) = 0

Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3
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 = {-3, 5}