12z+12-2z^2+2=6z-6

Solution for 12z+12-2z^2+2=6z-6 equation:

Simplifying
12z + 12 + -2z2 + 2 = 6z + -6

Reorder the terms:
12 + 2 + 12z + -2z2 = 6z + -6

Combine like terms: 12 + 2 = 14
14 + 12z + -2z2 = 6z + -6

Reorder the terms:
14 + 12z + -2z2 = -6 + 6z

Solving
14 + 12z + -2z2 = -6 + 6z

Solving for variable 'z'.

Reorder the terms:
14 + 6 + 12z + -6z + -2z2 = -6 + 6z + 6 + -6z

Combine like terms: 14 + 6 = 20
20 + 12z + -6z + -2z2 = -6 + 6z + 6 + -6z

Combine like terms: 12z + -6z = 6z
20 + 6z + -2z2 = -6 + 6z + 6 + -6z

Reorder the terms:
20 + 6z + -2z2 = -6 + 6 + 6z + -6z

Combine like terms: -6 + 6 = 0
20 + 6z + -2z2 = 0 + 6z + -6z
20 + 6z + -2z2 = 6z + -6z

Combine like terms: 6z + -6z = 0
20 + 6z + -2z2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + 3z + -1z2) = 0

Factor a trinomial.
2((5 + -1z)(2 + z)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + -1z)' equal to zero and attempt to solve:

Simplifying
5 + -1z = 0

Solving
5 + -1z = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1z = 0 + -5
-1z = 0 + -5

Combine like terms: 0 + -5 = -5
-1z = -5

Divide each side by '-1'.
z = 5

Simplifying
z = 5
Subproblem 2
Set the factor '(2 + z)' equal to zero and attempt to solve:

Simplifying
2 + z = 0

Solving
2 + z = 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 + z = 0 + -2

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

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

Simplifying
z = -2
Solution
z = {5, -2}