2z^2-10z-6=0

Solution for 2z^2-10z-6=0 equation:

Simplifying
2z2 + -10z + -6 = 0

Reorder the terms:
-6 + -10z + 2z2 = 0

Solving
-6 + -10z + 2z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -5z + z2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -5z + z2)' equal to zero and attempt to solve:

Simplifying
-3 + -5z + z2 = 0

Solving
-3 + -5z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -5z + 3 + z2 = 0 + 3

Reorder the terms:
-3 + 3 + -5z + z2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5z + z2 = 0 + 3
-5z + z2 = 0 + 3

Combine like terms: 0 + 3 = 3
-5z + z2 = 3

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 = 3 + 6.25

Reorder the terms:
6.25 + -5z + z2 = 3 + 6.25

Combine like terms: 3 + 6.25 = 9.25
6.25 + -5z + z2 = 9.25

Factor a perfect square on the left side:
(z + -2.5)(z + -2.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(z + -2.5) equal to 3.041381265 and -3.041381265.

Subproblem 1
z + -2.5 = 3.041381265

Simplifying
z + -2.5 = 3.041381265

Reorder the terms:
-2.5 + z = 3.041381265

Solving
-2.5 + z = 3.041381265

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 = 3.041381265 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + z = 3.041381265 + 2.5
z = 3.041381265 + 2.5

Combine like terms: 3.041381265 + 2.5 = 5.541381265
z = 5.541381265

Simplifying
z = 5.541381265

Subproblem 2
z + -2.5 = -3.041381265

Simplifying
z + -2.5 = -3.041381265

Reorder the terms:
-2.5 + z = -3.041381265

Solving
-2.5 + z = -3.041381265

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 = -3.041381265 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + z = -3.041381265 + 2.5
z = -3.041381265 + 2.5

Combine like terms: -3.041381265 + 2.5 = -0.541381265
z = -0.541381265

Simplifying
z = -0.541381265

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {5.541381265, -0.541381265}
Solution
z = {5.541381265, -0.541381265}