0=24(-5-x)(6-x)

Solution for 0=24(-5-x)(6-x) equation:

Simplifying
0 = 24(-5 + -1x)(6 + -1x)

Multiply (-5 + -1x) * (6 + -1x)
0 = 24(-5(6 + -1x) + -1x * (6 + -1x))
0 = 24((6 * -5 + -1x * -5) + -1x * (6 + -1x))
0 = 24((-30 + 5x) + -1x * (6 + -1x))
0 = 24(-30 + 5x + (6 * -1x + -1x * -1x))
0 = 24(-30 + 5x + (-6x + 1x2))

Combine like terms: 5x + -6x = -1x
0 = 24(-30 + -1x + 1x2)
0 = (-30 * 24 + -1x * 24 + 1x2 * 24)
0 = (-720 + -24x + 24x2)

Solving
0 = -720 + -24x + 24x2

Solving for variable 'x'.

Combine like terms: 0 + 720 = 720
720 + 24x + -24x2 = -720 + -24x + 24x2 + 720 + 24x + -24x2

Reorder the terms:
720 + 24x + -24x2 = -720 + 720 + -24x + 24x + 24x2 + -24x2

Combine like terms: -720 + 720 = 0
720 + 24x + -24x2 = 0 + -24x + 24x + 24x2 + -24x2
720 + 24x + -24x2 = -24x + 24x + 24x2 + -24x2

Combine like terms: -24x + 24x = 0
720 + 24x + -24x2 = 0 + 24x2 + -24x2
720 + 24x + -24x2 = 24x2 + -24x2

Combine like terms: 24x2 + -24x2 = 0
720 + 24x + -24x2 = 0

Factor out the Greatest Common Factor (GCF), '24'.
24(30 + x + -1x2) = 0

Factor a trinomial.
24((6 + -1x)(5 + x)) = 0

Ignore the factor 24.
Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 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 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Solution
x = {6, -5}