z^2+10z+25=256

Solution for z^2+10z+25=256 equation:

Simplifying
z2 + 10z + 25 = 256

Reorder the terms:
25 + 10z + z2 = 256

Solving
25 + 10z + z2 = 256

Solving for variable 'z'.

Reorder the terms:
25 + -256 + 10z + z2 = 256 + -256

Combine like terms: 25 + -256 = -231
-231 + 10z + z2 = 256 + -256

Combine like terms: 256 + -256 = 0
-231 + 10z + z2 = 0

Factor a trinomial.
(-21 + -1z)(11 + -1z) = 0

Subproblem 1
Set the factor '(-21 + -1z)' equal to zero and attempt to solve:

Simplifying
-21 + -1z = 0

Solving
-21 + -1z = 0

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

Add '21' to each side of the equation.
-21 + 21 + -1z = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -1z = 0 + 21
-1z = 0 + 21

Combine like terms: 0 + 21 = 21
-1z = 21

Divide each side by '-1'.
z = -21

Simplifying
z = -21
Subproblem 2
Set the factor '(11 + -1z)' equal to zero and attempt to solve:

Simplifying
11 + -1z = 0

Solving
11 + -1z = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1z = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1z = 0 + -11
-1z = 0 + -11

Combine like terms: 0 + -11 = -11
-1z = -11

Divide each side by '-1'.
z = 11

Simplifying
z = 11
Solution
z = {-21, 11}