z^2=-19z-90

Solution for z^2=-19z-90 equation:

Simplifying
z2 = -19z + -90

Reorder the terms:
z2 = -90 + -19z

Solving
z2 = -90 + -19z

Solving for variable 'z'.

Reorder the terms:
90 + 19z + z2 = -90 + -19z + 90 + 19z

Reorder the terms:
90 + 19z + z2 = -90 + 90 + -19z + 19z

Combine like terms: -90 + 90 = 0
90 + 19z + z2 = 0 + -19z + 19z
90 + 19z + z2 = -19z + 19z

Combine like terms: -19z + 19z = 0
90 + 19z + z2 = 0

Factor a trinomial.
(10 + z)(9 + z) = 0

Subproblem 1
Set the factor '(10 + z)' equal to zero and attempt to solve:

Simplifying
10 + z = 0

Solving
10 + z = 0

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

Add '-10' to each side of the equation.
10 + -10 + z = 0 + -10

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

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

Simplifying
z = -10
Subproblem 2
Set the factor '(9 + z)' equal to zero and attempt to solve:

Simplifying
9 + z = 0

Solving
9 + z = 0

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

Add '-9' to each side of the equation.
9 + -9 + z = 0 + -9

Combine like terms: 9 + -9 = 0
0 + z = 0 + -9
z = 0 + -9

Combine like terms: 0 + -9 = -9
z = -9

Simplifying
z = -9
Solution
z = {-10, -9}