2+8z^2=6z

Solution for 2+8z^2=6z equation:

Simplifying
2 + 8z2 = 6z

Solving
2 + 8z2 = 6z

Solving for variable 'z'.

Reorder the terms:
2 + -6z + 8z2 = 6z + -6z

Combine like terms: 6z + -6z = 0
2 + -6z + 8z2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -3z + 4z2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + -3z + 4z2)' equal to zero and attempt to solve:

Simplifying
1 + -3z + 4z2 = 0

Solving
1 + -3z + 4z2 = 0

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
0.25 + -0.75z + z2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -0.75z + -0.25 + z2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -0.75z + z2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -0.75z + z2 = 0 + -0.25
-0.75z + z2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-0.75z + z2 = -0.25

The z term is -0.75z.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75z + 0.140625 + z2 = -0.25 + 0.140625

Reorder the terms:
0.140625 + -0.75z + z2 = -0.25 + 0.140625

Combine like terms: -0.25 + 0.140625 = -0.109375
0.140625 + -0.75z + z2 = -0.109375

Factor a perfect square on the left side:
(z + -0.375)(z + -0.375) = -0.109375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.