64z^4-80z^3-24z^2=0

Solution for 64z^4-80z^3-24z^2=0 equation:

Simplifying
64z4 + -80z3 + -24z2 = 0

Reorder the terms:
-24z2 + -80z3 + 64z4 = 0

Solving
-24z2 + -80z3 + 64z4 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '8z2'.
8z2(-3 + -10z + 8z2) = 0

Factor a trinomial.
8z2((-1 + -4z)(3 + -2z)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor 'z2' equal to zero and attempt to solve:

Simplifying
z2 = 0

Solving
z2 = 0

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

Simplifying
z2 = 0

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

Simplifying
-1 + -4z = 0

Solving
-1 + -4z = 0

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

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

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

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

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

Simplifying
z = -0.25
Subproblem 3
Set the factor '(3 + -2z)' equal to zero and attempt to solve:

Simplifying
3 + -2z = 0

Solving
3 + -2z = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2z = 0 + -3
-2z = 0 + -3

Combine like terms: 0 + -3 = -3
-2z = -3

Divide each side by '-2'.
z = 1.5

Simplifying
z = 1.5
Solution
z = {0, -0.25, 1.5}