7z^4-35z^3-14z^2=

Solution for 7z^4-35z^3-14z^2= equation:

Simplifying
7z4 + -35z3 + -14z2 = 0

Reorder the terms:
-14z2 + -35z3 + 7z4 = 0

Solving
-14z2 + -35z3 + 7z4 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '7z2'.
7z2(-2 + -5z + z2) = 0

Ignore the factor 7.
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 '(-2 + -5z + z2)' equal to zero and attempt to solve:

Simplifying
-2 + -5z + z2 = 0

Solving
-2 + -5z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -5z + 2 + z2 = 0 + 2

Reorder the terms:
-2 + 2 + -5z + z2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -5z + z2 = 0 + 2
-5z + z2 = 0 + 2

Combine like terms: 0 + 2 = 2
-5z + z2 = 2

The z term is -5z.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5z + 6.25 + z2 = 2 + 6.25

Reorder the terms:
6.25 + -5z + z2 = 2 + 6.25

Combine like terms: 2 + 6.25 = 8.25
6.25 + -5z + z2 = 8.25

Factor a perfect square on the left side:
(z + -2.5)(z + -2.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(z + -2.5) equal to 2.872281323 and -2.872281323.

Subproblem 1
z + -2.5 = 2.872281323

Simplifying
z + -2.5 = 2.872281323

Reorder the terms:
-2.5 + z = 2.872281323

Solving
-2.5 + z = 2.872281323

Solving for variable 'z'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + z = 2.872281323 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + z = 2.872281323 + 2.5
z = 2.872281323 + 2.5

Combine like terms: 2.872281323 + 2.5 = 5.372281323
z = 5.372281323

Simplifying
z = 5.372281323

Subproblem 2
z + -2.5 = -2.872281323

Simplifying
z + -2.5 = -2.872281323

Reorder the terms:
-2.5 + z = -2.872281323

Solving
-2.5 + z = -2.872281323

Solving for variable 'z'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + z = -2.872281323 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + z = -2.872281323 + 2.5
z = -2.872281323 + 2.5

Combine like terms: -2.872281323 + 2.5 = -0.372281323
z = -0.372281323

Simplifying
z = -0.372281323

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {5.372281323, -0.372281323}
Solution
z = {0, 5.372281323, -0.372281323}