z^2+5z=30+6z

Solution for z^2+5z=30+6z equation:

Simplifying
z2 + 5z = 30 + 6z

Reorder the terms:
5z + z2 = 30 + 6z

Solving
5z + z2 = 30 + 6z

Solving for variable 'z'.

Reorder the terms:
-30 + 5z + -6z + z2 = 30 + 6z + -30 + -6z

Combine like terms: 5z + -6z = -1z
-30 + -1z + z2 = 30 + 6z + -30 + -6z

Reorder the terms:
-30 + -1z + z2 = 30 + -30 + 6z + -6z

Combine like terms: 30 + -30 = 0
-30 + -1z + z2 = 0 + 6z + -6z
-30 + -1z + z2 = 6z + -6z

Combine like terms: 6z + -6z = 0
-30 + -1z + z2 = 0

Factor a trinomial.
(-5 + -1z)(6 + -1z) = 0

Subproblem 1
Set the factor '(-5 + -1z)' equal to zero and attempt to solve:

Simplifying
-5 + -1z = 0

Solving
-5 + -1z = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1z = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1z = 0 + 5
-1z = 0 + 5

Combine like terms: 0 + 5 = 5
-1z = 5

Divide each side by '-1'.
z = -5

Simplifying
z = -5
Subproblem 2
Set the factor '(6 + -1z)' equal to zero and attempt to solve:

Simplifying
6 + -1z = 0

Solving
6 + -1z = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1z = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1z = 0 + -6
-1z = 0 + -6

Combine like terms: 0 + -6 = -6
-1z = -6

Divide each side by '-1'.
z = 6

Simplifying
z = 6
Solution
z = {-5, 6}