(x-5)(x-3)=24

Solution for (x-5)(x-3)=24 equation:

Simplifying
(x + -5)(x + -3) = 24

Reorder the terms:
(-5 + x)(x + -3) = 24

Reorder the terms:
(-5 + x)(-3 + x) = 24

Multiply (-5 + x) * (-3 + x)
(-5(-3 + x) + x(-3 + x)) = 24
((-3 * -5 + x * -5) + x(-3 + x)) = 24
((15 + -5x) + x(-3 + x)) = 24
(15 + -5x + (-3 * x + x * x)) = 24
(15 + -5x + (-3x + x2)) = 24

Combine like terms: -5x + -3x = -8x
(15 + -8x + x2) = 24

Solving
15 + -8x + x2 = 24

Solving for variable 'x'.

Reorder the terms:
15 + -24 + -8x + x2 = 24 + -24

Combine like terms: 15 + -24 = -9
-9 + -8x + x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-9 + -8x + x2 = 0

Factor a trinomial.
(-1 + -1x)(9 + -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 '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-1, 9}