4z=2z^2-6

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

Simplifying
4z = 2z2 + -6

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

Solving
4z = -6 + 2z2

Solving for variable 'z'.

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

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

Combine like terms: -6 + 6 = 0
6 + 4z + -2z2 = 0 + 2z2 + -2z2
6 + 4z + -2z2 = 2z2 + -2z2

Combine like terms: 2z2 + -2z2 = 0
6 + 4z + -2z2 = 0

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

Factor a trinomial.
2((3 + -1z)(1 + 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 '(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
Solution
z = {3, -1}