-16x^3-8x^2=0

Solution for -16x^3-8x^2=0 equation:

Simplifying
-16x3 + -8x2 = 0

Reorder the terms:
-8x2 + -16x3 = 0

Solving
-8x2 + -16x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-8x2'.
-8x2(1 + 2x) = 0

Ignore the factor -8.
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 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 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 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {0, -0.5}