16g^4-8g^3+g^2=0

Solution for 16g^4-8g^3+g^2=0 equation:

Simplifying
16g4 + -8g3 + g2 = 0

Reorder the terms:
g2 + -8g3 + 16g4 = 0

Solving
g2 + -8g3 + 16g4 = 0

Solving for variable 'g'.

Factor out the Greatest Common Factor (GCF), 'g2'.
g2(1 + -8g + 16g2) = 0

Factor a trinomial.
g2((1 + -4g)(1 + -4g)) = 0

Subproblem 1
Set the factor 'g2' equal to zero and attempt to solve:

Simplifying
g2 = 0

Solving
g2 = 0

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

Simplifying
g2 = 0

Take the square root of each side:
g = {0}
Subproblem 2
Set the factor '(1 + -4g)' equal to zero and attempt to solve:

Simplifying
1 + -4g = 0

Solving
1 + -4g = 0

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

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

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

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

Divide each side by '-4'.
g = 0.25

Simplifying
g = 0.25
Subproblem 3
Set the factor '(1 + -4g)' equal to zero and attempt to solve:

Simplifying
1 + -4g = 0

Solving
1 + -4g = 0

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

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

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

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

Divide each side by '-4'.
g = 0.25

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