z(3z+2)=z^2+4

Solution for z(3z+2)=z^2+4 equation:

Simplifying
z(3z + 2) = z2 + 4

Reorder the terms:
z(2 + 3z) = z2 + 4
(2 * z + 3z * z) = z2 + 4
(2z + 3z2) = z2 + 4

Reorder the terms:
2z + 3z2 = 4 + z2

Solving
2z + 3z2 = 4 + z2

Solving for variable 'z'.

Reorder the terms:
-4 + 2z + 3z2 + -1z2 = 4 + z2 + -4 + -1z2

Combine like terms: 3z2 + -1z2 = 2z2
-4 + 2z + 2z2 = 4 + z2 + -4 + -1z2

Reorder the terms:
-4 + 2z + 2z2 = 4 + -4 + z2 + -1z2

Combine like terms: 4 + -4 = 0
-4 + 2z + 2z2 = 0 + z2 + -1z2
-4 + 2z + 2z2 = z2 + -1z2

Combine like terms: z2 + -1z2 = 0
-4 + 2z + 2z2 = 0

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

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

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

Simplifying
-2 + -1z = 0

Solving
-2 + -1z = 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 + -1z = 0 + 2

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

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

Divide each side by '-1'.
z = -2

Simplifying
z = -2
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 = {-2, 1}