3z(2z-2)=-6(z^2-2)-6

Solution for 3z(2z-2)=-6(z^2-2)-6 equation:

Simplifying
3z(2z + -2) = -6(z2 + -2) + -6

Reorder the terms:
3z(-2 + 2z) = -6(z2 + -2) + -6
(-2 * 3z + 2z * 3z) = -6(z2 + -2) + -6
(-6z + 6z2) = -6(z2 + -2) + -6

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

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

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

Solving
-6z + 6z2 = 6 + -6z2

Solving for variable 'z'.

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), '6'.
6(-1 + -1z + 2z2) = 0

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

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

Simplifying
1 + -1z = 0

Solving
1 + -1z = 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 + -1z = 0 + -1

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

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

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

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