x^2(72-x)=0

Solution for x^2(72-x)=0 equation:

Simplifying
x2(72 + -1x) = 0
(72 * x2 + -1x * x2) = 0
(72x2 + -1x3) = 0

Solving
72x2 + -1x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(72 + -1x) = 0

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}
Subproblem 2
Set the factor '(72 + -1x)' equal to zero and attempt to solve:

Simplifying
72 + -1x = 0

Solving
72 + -1x = 0

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

Add '-72' to each side of the equation.
72 + -72 + -1x = 0 + -72

Combine like terms: 72 + -72 = 0
0 + -1x = 0 + -72
-1x = 0 + -72

Combine like terms: 0 + -72 = -72
-1x = -72

Divide each side by '-1'.
x = 72

Simplifying
x = 72
Solution
x = {0, 72}