-4z^2-z=2

Solution for -4z^2-z=2 equation:

Simplifying
-4z2 + -1z = 2

Reorder the terms:
-1z + -4z2 = 2

Solving
-1z + -4z2 = 2

Solving for variable 'z'.

Reorder the terms:
-2 + -1z + -4z2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -1z + -4z2 = 0

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

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

Simplifying
2 + z + 4z2 = 0

Solving
2 + z + 4z2 = 0

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

Divide each side by '4'.
0.5 + 0.25z + z2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 0.25z + -0.5 + z2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 0.25z + z2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 0.25z + z2 = 0 + -0.5
0.25z + z2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
0.25z + z2 = -0.5

The z term is z.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.25z + 0.25 + z2 = -0.5 + 0.25

Reorder the terms:
0.25 + 0.25z + z2 = -0.5 + 0.25

Combine like terms: -0.5 + 0.25 = -0.25
0.25 + 0.25z + z2 = -0.25

Factor a perfect square on the left side:
(z + 0.5)(z + 0.5) = -0.25

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.