z^2+10z=-25

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

Simplifying
z2 + 10z = -25

Reorder the terms:
10z + z2 = -25

Solving
10z + z2 = -25

Solving for variable 'z'.

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

Combine like terms: -25 + 25 = 0
25 + 10z + z2 = 0

Factor a trinomial.
(5 + z)(5 + z) = 0

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

Simplifying
5 + z = 0

Solving
5 + z = 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 + z = 0 + -5

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

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

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

Simplifying
5 + z = 0

Solving
5 + z = 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 + z = 0 + -5

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

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

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