z^2+5z=50

Solution for z^2+5z=50 equation:

Simplifying
z2 + 5z = 50

Reorder the terms:
5z + z2 = 50

Solving
5z + z2 = 50

Solving for variable 'z'.

Reorder the terms:
-50 + 5z + z2 = 50 + -50

Combine like terms: 50 + -50 = 0
-50 + 5z + z2 = 0

Factor a trinomial.
(-10 + -1z)(5 + -1z) = 0

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

Simplifying
-10 + -1z = 0

Solving
-10 + -1z = 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 + -1z = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1z = 0 + 10
-1z = 0 + 10

Combine like terms: 0 + 10 = 10
-1z = 10

Divide each side by '-1'.
z = -10

Simplifying
z = -10
Subproblem 2
Set the factor '(5 + -1z)' equal to zero and attempt to solve:

Simplifying
5 + -1z = 0

Solving
5 + -1z = 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 + -1z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1z = 0 + -5
-1z = 0 + -5

Combine like terms: 0 + -5 = -5
-1z = -5

Divide each side by '-1'.
z = 5

Simplifying
z = 5
Solution
z = {-10, 5}