8x(x-5)-24(x-5)=0

Solution for 8x(x-5)-24(x-5)=0 equation:

Simplifying
8x(x + -5) + -24(x + -5) = 0

Reorder the terms:
8x(-5 + x) + -24(x + -5) = 0
(-5 * 8x + x * 8x) + -24(x + -5) = 0
(-40x + 8x2) + -24(x + -5) = 0

Reorder the terms:
-40x + 8x2 + -24(-5 + x) = 0
-40x + 8x2 + (-5 * -24 + x * -24) = 0
-40x + 8x2 + (120 + -24x) = 0

Reorder the terms:
120 + -40x + -24x + 8x2 = 0

Combine like terms: -40x + -24x = -64x
120 + -64x + 8x2 = 0

Solving
120 + -64x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(15 + -8x + x2) = 0

Factor a trinomial.
8((3 + -1x)(5 + -1x)) = 0

Ignore the factor 8.
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}