0=z^2+4z-12

Solution for 0=z^2+4z-12 equation:

Simplifying
0 = z2 + 4z + -12

Reorder the terms:
0 = -12 + 4z + z2

Solving
0 = -12 + 4z + z2

Solving for variable 'z'.

Combine like terms: 0 + 12 = 12
12 + -4z + -1z2 = -12 + 4z + z2 + 12 + -4z + -1z2

Reorder the terms:
12 + -4z + -1z2 = -12 + 12 + 4z + -4z + z2 + -1z2

Combine like terms: -12 + 12 = 0
12 + -4z + -1z2 = 0 + 4z + -4z + z2 + -1z2
12 + -4z + -1z2 = 4z + -4z + z2 + -1z2

Combine like terms: 4z + -4z = 0
12 + -4z + -1z2 = 0 + z2 + -1z2
12 + -4z + -1z2 = z2 + -1z2

Combine like terms: z2 + -1z2 = 0
12 + -4z + -1z2 = 0

Factor a trinomial.
(2 + -1z)(6 + z) = 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 + z)' equal to zero and attempt to solve:

Simplifying
6 + z = 0

Solving
6 + z = 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 + z = 0 + -6

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

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

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