z^2-10z+10=-11

Solution for z^2-10z+10=-11 equation:

Simplifying
z2 + -10z + 10 = -11

Reorder the terms:
10 + -10z + z2 = -11

Solving
10 + -10z + z2 = -11

Solving for variable 'z'.

Reorder the terms:
10 + 11 + -10z + z2 = -11 + 11

Combine like terms: 10 + 11 = 21
21 + -10z + z2 = -11 + 11

Combine like terms: -11 + 11 = 0
21 + -10z + z2 = 0

Factor a trinomial.
(3 + -1z)(7 + -1z) = 0

Subproblem 1
Set the factor '(3 + -1z)' equal to zero and attempt to solve:

Simplifying
3 + -1z = 0

Solving
3 + -1z = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1z = 0 + -3

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

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

Divide each side by '-1'.
z = 3

Simplifying
z = 3
Subproblem 2
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
Solution
z = {3, 7}