4z^2=4(z-6)

Solution for 4z^2=4(z-6) equation:

Simplifying
4z2 = 4(z + -6)

Reorder the terms:
4z2 = 4(-6 + z)
4z2 = (-6 * 4 + z * 4)
4z2 = (-24 + 4z)

Solving
4z2 = -24 + 4z

Solving for variable 'z'.

Reorder the terms:
24 + -4z + 4z2 = -24 + 4z + 24 + -4z

Reorder the terms:
24 + -4z + 4z2 = -24 + 24 + 4z + -4z

Combine like terms: -24 + 24 = 0
24 + -4z + 4z2 = 0 + 4z + -4z
24 + -4z + 4z2 = 4z + -4z

Combine like terms: 4z + -4z = 0
24 + -4z + 4z2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(6 + -1z + z2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(6 + -1z + z2)' equal to zero and attempt to solve:

Simplifying
6 + -1z + z2 = 0

Solving
6 + -1z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -1z + -6 + z2 = 0 + -6

Reorder the terms:
6 + -6 + -1z + z2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1z + z2 = 0 + -6
-1z + z2 = 0 + -6

Combine like terms: 0 + -6 = -6
-1z + z2 = -6

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 = -6 + 0.25

Reorder the terms:
0.25 + -1z + z2 = -6 + 0.25

Combine like terms: -6 + 0.25 = -5.75
0.25 + -1z + z2 = -5.75

Factor a perfect square on the left side:
(z + -0.5)(z + -0.5) = -5.75

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.