0=x^3-8x^2

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Solution for 0=x^3-8x^2 equation: 


Simplifying
0 = x3 + -8x2

Reorder the terms:
0 = -8x2 + x3

Solving
0 = -8x2 + x3

Solving for variable 'x'.
Remove the zero:
8x2 + -1x3 = -8x2 + x3 + 8x2 + -1x3

Reorder the terms:
8x2 + -1x3 = -8x2 + 8x2 + x3 + -1x3

Combine like terms: -8x2 + 8x2 = 0
8x2 + -1x3 = 0 + x3 + -1x3
8x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
8x2 + -1x3 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(8 + -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 '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {0, 8}

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