-2z^2+6z+12=4z

Solution for -2z^2+6z+12=4z equation:

Simplifying
-2z2 + 6z + 12 = 4z

Reorder the terms:
12 + 6z + -2z2 = 4z

Solving
12 + 6z + -2z2 = 4z

Solving for variable 'z'.

Reorder the terms:
12 + 6z + -4z + -2z2 = 4z + -4z

Combine like terms: 6z + -4z = 2z
12 + 2z + -2z2 = 4z + -4z

Combine like terms: 4z + -4z = 0
12 + 2z + -2z2 = 0

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

Factor a trinomial.
2((3 + -1z)(2 + z)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -1z)' equal to zero and attempt to solve:

Simplifying
3 + -1z = 0

Solving
3 + -1z = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1z = 0 + -3
-1z = 0 + -3

Combine like terms: 0 + -3 = -3
-1z = -3

Divide each side by '-1'.
z = 3

Simplifying
z = 3
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 = {3, -2}