z^2=4(2z-3)

Solution for z^2=4(2z-3) equation:

Simplifying
z2 = 4(2z + -3)

Reorder the terms:
z2 = 4(-3 + 2z)
z2 = (-3 * 4 + 2z * 4)
z2 = (-12 + 8z)

Solving
z2 = -12 + 8z

Solving for variable 'z'.

Reorder the terms:
12 + -8z + z2 = -12 + 8z + 12 + -8z

Reorder the terms:
12 + -8z + z2 = -12 + 12 + 8z + -8z

Combine like terms: -12 + 12 = 0
12 + -8z + z2 = 0 + 8z + -8z
12 + -8z + z2 = 8z + -8z

Combine like terms: 8z + -8z = 0
12 + -8z + z2 = 0

Factor a trinomial.
(2 + -1z)(6 + -1z) = 0

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

Simplifying
2 + -1z = 0

Solving
2 + -1z = 0

Move all terms containing z to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1z = 0 + -2

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

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

Divide each side by '-1'.
z = 2

Simplifying
z = 2
Subproblem 2
Set the factor '(6 + -1z)' equal to zero and attempt to solve:

Simplifying
6 + -1z = 0

Solving
6 + -1z = 0

Move all terms containing z to the left, all other terms to the right.

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

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

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

Divide each side by '-1'.
z = 6

Simplifying
z = 6
Solution
z = {2, 6}