x^3=1.5x^2

Solution for x^3=1.5x^2 equation:

Simplifying
x3 = 1.5x2

Solving
x3 = 1.5x2

Solving for variable 'x'.

Reorder the terms:
-1.5x2 + x3 = 1.5x2 + -1.5x2

Combine like terms: 1.5x2 + -1.5x2 = 0.0
-1.5x2 + x3 = 0.0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-1.5 + x) = 0.0

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 '(-1.5 + x)' equal to zero and attempt to solve:

Simplifying
-1.5 + x = 0

Solving
-1.5 + x = 0

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 0 + 1.5
x = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
x = 1.5

Simplifying
x = 1.5
Solution
x = {0, 1.5}