4(z-1)2z=-4

Solution for 4(z-1)2z=-4 equation:

Simplifying
4(z + -1) * 2z = -4

Reorder the terms:
4(-1 + z) * 2z = -4

Reorder the terms for easier multiplication:
4 * 2z(-1 + z) = -4

Multiply 4 * 2
8z(-1 + z) = -4
(-1 * 8z + z * 8z) = -4
(-8z + 8z2) = -4

Solving
-8z + 8z2 = -4

Solving for variable 'z'.

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

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

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

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

Simplifying
1 + -2z + 2z2 = 0

Solving
1 + -2z + 2z2 = 0

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

Divide each side by '2'.
0.5 + -1z + z2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -1z + -0.5 + z2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -1z + z2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -1z + z2 = 0 + -0.5
-1z + z2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-1z + z2 = -0.5

The z term is -1z.  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.
-1z + 0.25 + z2 = -0.5 + 0.25

Reorder the terms:
0.25 + -1z + z2 = -0.5 + 0.25

Combine like terms: -0.5 + 0.25 = -0.25
0.25 + -1z + 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.