4z^3-8z=14z^2

Solution for 4z^3-8z=14z^2 equation:

Simplifying
4z3 + -8z = 14z2

Reorder the terms:
-8z + 4z3 = 14z2

Solving
-8z + 4z3 = 14z2

Solving for variable 'z'.

Reorder the terms:
-8z + -14z2 + 4z3 = 14z2 + -14z2

Combine like terms: 14z2 + -14z2 = 0
-8z + -14z2 + 4z3 = 0

Factor out the Greatest Common Factor (GCF), '2z'.
2z(-4 + -7z + 2z2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor 'z' equal to zero and attempt to solve:

Simplifying
z = 0

Solving
z = 0

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

Simplifying
z = 0
Subproblem 2
Set the factor '(-1 + -2z)' equal to zero and attempt to solve:

Simplifying
-1 + -2z = 0

Solving
-1 + -2z = 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 + -2z = 0 + 1

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

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

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

Simplifying
z = -0.5
Subproblem 3
Set the factor '(4 + -1z)' equal to zero and attempt to solve:

Simplifying
4 + -1z = 0

Solving
4 + -1z = 0

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

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

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

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

Divide each side by '-1'.
z = 4

Simplifying
z = 4
Solution
z = {0, -0.5, 4}