2(12z^2+6z+12z+6)=

Solution for 2(12z^2+6z+12z+6)= equation:

Simplifying
2(12z2 + 6z + 12z + 6) = 0

Reorder the terms:
2(6 + 6z + 12z + 12z2) = 0

Combine like terms: 6z + 12z = 18z
2(6 + 18z + 12z2) = 0
(6 * 2 + 18z * 2 + 12z2 * 2) = 0
(12 + 36z + 24z2) = 0

Solving
12 + 36z + 24z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '12'.
12(1 + 3z + 2z2) = 0

Factor a trinomial.
12((1 + z)(1 + 2z)) = 0

Ignore the factor 12.
Subproblem 1
Set the factor '(1 + z)' equal to zero and attempt to solve:

Simplifying
1 + z = 0

Solving
1 + z = 0

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

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

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

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

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

Simplifying
1 + 2z = 0

Solving
1 + 2z = 0

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

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

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

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

Divide each side by '2'.
z = -0.5

Simplifying
z = -0.5
Solution
z = {-1, -0.5}