z^2+65z+1000=0

Solution for z^2+65z+1000=0 equation:

Simplifying
z2 + 65z + 1000 = 0

Reorder the terms:
1000 + 65z + z2 = 0

Solving
1000 + 65z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(40 + z)(25 + z) = 0

Subproblem 1
Set the factor '(40 + z)' equal to zero and attempt to solve:

Simplifying
40 + z = 0

Solving
40 + z = 0

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

Add '-40' to each side of the equation.
40 + -40 + z = 0 + -40

Combine like terms: 40 + -40 = 0
0 + z = 0 + -40
z = 0 + -40

Combine like terms: 0 + -40 = -40
z = -40

Simplifying
z = -40
Subproblem 2
Set the factor '(25 + z)' equal to zero and attempt to solve:

Simplifying
25 + z = 0

Solving
25 + z = 0

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

Add '-25' to each side of the equation.
25 + -25 + z = 0 + -25

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

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

Simplifying
z = -25
Solution
z = {-40, -25}