z^2-6=4z+6

Solution for z^2-6=4z+6 equation:

Simplifying
z2 + -6 = 4z + 6

Reorder the terms:
-6 + z2 = 4z + 6

Reorder the terms:
-6 + z2 = 6 + 4z

Solving
-6 + z2 = 6 + 4z

Solving for variable 'z'.

Reorder the terms:
-6 + -6 + -4z + z2 = 6 + 4z + -6 + -4z

Combine like terms: -6 + -6 = -12
-12 + -4z + z2 = 6 + 4z + -6 + -4z

Reorder the terms:
-12 + -4z + z2 = 6 + -6 + 4z + -4z

Combine like terms: 6 + -6 = 0
-12 + -4z + z2 = 0 + 4z + -4z
-12 + -4z + z2 = 4z + -4z

Combine like terms: 4z + -4z = 0
-12 + -4z + 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}