16s^4-12s^3+24s^2=0

Solution for 16s^4-12s^3+24s^2=0 equation:

Simplifying
16s4 + -12s3 + 24s2 = 0

Reorder the terms:
24s2 + -12s3 + 16s4 = 0

Solving
24s2 + -12s3 + 16s4 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), '4s2'.
4s2(6 + -3s + 4s2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 's2' equal to zero and attempt to solve:

Simplifying
s2 = 0

Solving
s2 = 0

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

Simplifying
s2 = 0

Take the square root of each side:
s = {0}
Subproblem 2
Set the factor '(6 + -3s + 4s2)' equal to zero and attempt to solve:

Simplifying
6 + -3s + 4s2 = 0

Solving
6 + -3s + 4s2 = 0

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
1.5 + -0.75s + s2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -0.75s + -1.5 + s2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -0.75s + s2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -0.75s + s2 = 0 + -1.5
-0.75s + s2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-0.75s + s2 = -1.5

The s term is -0.75s.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75s + 0.140625 + s2 = -1.5 + 0.140625

Reorder the terms:
0.140625 + -0.75s + s2 = -1.5 + 0.140625

Combine like terms: -1.5 + 0.140625 = -1.359375
0.140625 + -0.75s + s2 = -1.359375

Factor a perfect square on the left side:
(s + -0.375)(s + -0.375) = -1.359375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
s = {0}