x(24x-72)-10(24x-72)=0

Solution for x(24x-72)-10(24x-72)=0 equation:

Simplifying
x(24x + -72) + -10(24x + -72) = 0

Reorder the terms:
x(-72 + 24x) + -10(24x + -72) = 0
(-72 * x + 24x * x) + -10(24x + -72) = 0
(-72x + 24x2) + -10(24x + -72) = 0

Reorder the terms:
-72x + 24x2 + -10(-72 + 24x) = 0
-72x + 24x2 + (-72 * -10 + 24x * -10) = 0
-72x + 24x2 + (720 + -240x) = 0

Reorder the terms:
720 + -72x + -240x + 24x2 = 0

Combine like terms: -72x + -240x = -312x
720 + -312x + 24x2 = 0

Solving
720 + -312x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '24'.
24(30 + -13x + x2) = 0

Factor a trinomial.
24((3 + -1x)(10 + -1x)) = 0

Ignore the factor 24.
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 '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {3, 10}