z^2+10z+35=-2z

Solution for z^2+10z+35=-2z equation:

Simplifying
z2 + 10z + 35 = -2z

Reorder the terms:
35 + 10z + z2 = -2z

Solving
35 + 10z + z2 = -2z

Solving for variable 'z'.

Reorder the terms:
35 + 10z + 2z + z2 = -2z + 2z

Combine like terms: 10z + 2z = 12z
35 + 12z + z2 = -2z + 2z

Combine like terms: -2z + 2z = 0
35 + 12z + z2 = 0

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

Subproblem 1
Set the factor '(7 + z)' equal to zero and attempt to solve:

Simplifying
7 + z = 0

Solving
7 + z = 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 + z = 0 + -7

Combine like terms: 7 + -7 = 0
0 + z = 0 + -7
z = 0 + -7

Combine like terms: 0 + -7 = -7
z = -7

Simplifying
z = -7
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 = {-7, -5}