8x^3=2x^2

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

Simplifying
8x3 = 2x2

Solving
8x3 = 2x2

Solving for variable 'x'.

Reorder the terms:
-2x2 + 8x3 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-2x2 + 8x3 = 0

Factor out the Greatest Common Factor (GCF), '2x2'.
2x2(-1 + 4x) = 0

Ignore the factor 2.
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 + 4x)' equal to zero and attempt to solve:

Simplifying
-1 + 4x = 0

Solving
-1 + 4x = 0

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

Add '1' to each side of the equation.
-1 + 1 + 4x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 4x = 0 + 1
4x = 0 + 1

Combine like terms: 0 + 1 = 1
4x = 1

Divide each side by '4'.
x = 0.25

Simplifying
x = 0.25
Solution
x = {0, 0.25}