z^2+2=6+3z

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

Simplifying
z2 + 2 = 6 + 3z

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

Solving
2 + z2 = 6 + 3z

Solving for variable 'z'.

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

Combine like terms: 2 + -6 = -4
-4 + -3z + z2 = 6 + 3z + -6 + -3z

Reorder the terms:
-4 + -3z + z2 = 6 + -6 + 3z + -3z

Combine like terms: 6 + -6 = 0
-4 + -3z + z2 = 0 + 3z + -3z
-4 + -3z + z2 = 3z + -3z

Combine like terms: 3z + -3z = 0
-4 + -3z + z2 = 0

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

Subproblem 1
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
Subproblem 2
Set the factor '(4 + -1z)' equal to zero and attempt to solve:

Simplifying
4 + -1z = 0

Solving
4 + -1z = 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 + -1z = 0 + -4

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

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

Divide each side by '-1'.
z = 4

Simplifying
z = 4
Solution
z = {-1, 4}