z^2+20=12z

Solution for z^2+20=12z equation:

Simplifying
z2 + 20 = 12z

Reorder the terms:
20 + z2 = 12z

Solving
20 + z2 = 12z

Solving for variable 'z'.

Reorder the terms:
20 + -12z + z2 = 12z + -12z

Combine like terms: 12z + -12z = 0
20 + -12z + z2 = 0

Factor a trinomial.
(2 + -1z)(10 + -1z) = 0

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 '(10 + -1z)' equal to zero and attempt to solve:

Simplifying
10 + -1z = 0

Solving
10 + -1z = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1z = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1z = 0 + -10
-1z = 0 + -10

Combine like terms: 0 + -10 = -10
-1z = -10

Divide each side by '-1'.
z = 10

Simplifying
z = 10
Solution
z = {2, 10}