z^2+2z=-14-7z

Solution for z^2+2z=-14-7z equation:

Simplifying
z2 + 2z = -14 + -7z

Reorder the terms:
2z + z2 = -14 + -7z

Solving
2z + z2 = -14 + -7z

Solving for variable 'z'.

Reorder the terms:
14 + 2z + 7z + z2 = -14 + -7z + 14 + 7z

Combine like terms: 2z + 7z = 9z
14 + 9z + z2 = -14 + -7z + 14 + 7z

Reorder the terms:
14 + 9z + z2 = -14 + 14 + -7z + 7z

Combine like terms: -14 + 14 = 0
14 + 9z + z2 = 0 + -7z + 7z
14 + 9z + z2 = -7z + 7z

Combine like terms: -7z + 7z = 0
14 + 9z + z2 = 0

Factor a trinomial.
(7 + z)(2 + 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 '(2 + z)' equal to zero and attempt to solve:

Simplifying
2 + z = 0

Solving
2 + z = 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 + z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + z = 0 + -2
z = 0 + -2

Combine like terms: 0 + -2 = -2
z = -2

Simplifying
z = -2
Solution
z = {-7, -2}