3z+34=z^2+6

Solution for 3z+34=z^2+6 equation:

Simplifying
3z + 34 = z2 + 6

Reorder the terms:
34 + 3z = z2 + 6

Reorder the terms:
34 + 3z = 6 + z2

Solving
34 + 3z = 6 + z2

Solving for variable 'z'.

Reorder the terms:
34 + -6 + 3z + -1z2 = 6 + z2 + -6 + -1z2

Combine like terms: 34 + -6 = 28
28 + 3z + -1z2 = 6 + z2 + -6 + -1z2

Reorder the terms:
28 + 3z + -1z2 = 6 + -6 + z2 + -1z2

Combine like terms: 6 + -6 = 0
28 + 3z + -1z2 = 0 + z2 + -1z2
28 + 3z + -1z2 = z2 + -1z2

Combine like terms: z2 + -1z2 = 0
28 + 3z + -1z2 = 0

Factor a trinomial.
(7 + -1z)(4 + z) = 0

Subproblem 1
Set the factor '(7 + -1z)' equal to zero and attempt to solve:

Simplifying
7 + -1z = 0

Solving
7 + -1z = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1z = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1z = 0 + -7
-1z = 0 + -7

Combine like terms: 0 + -7 = -7
-1z = -7

Divide each side by '-1'.
z = 7

Simplifying
z = 7
Subproblem 2
Set the factor '(4 + z)' equal to zero and attempt to solve:

Simplifying
4 + z = 0

Solving
4 + z = 0

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

Add '-4' to each side of the equation.
4 + -4 + z = 0 + -4

Combine like terms: 4 + -4 = 0
0 + z = 0 + -4
z = 0 + -4

Combine like terms: 0 + -4 = -4
z = -4

Simplifying
z = -4
Solution
z = {7, -4}