2=11z-5z^2

Solution for 2=11z-5z^2 equation:

Simplifying
2 = 11z + -5z2

Solving
2 = 11z + -5z2

Solving for variable 'z'.

Reorder the terms:
2 + -11z + 5z2 = 11z + -11z + -5z2 + 5z2

Combine like terms: 11z + -11z = 0
2 + -11z + 5z2 = 0 + -5z2 + 5z2
2 + -11z + 5z2 = -5z2 + 5z2

Combine like terms: -5z2 + 5z2 = 0
2 + -11z + 5z2 = 0

Factor a trinomial.
(1 + -5z)(2 + -1z) = 0

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

Simplifying
1 + -5z = 0

Solving
1 + -5z = 0

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

Add '-1' to each side of the equation.
1 + -1 + -5z = 0 + -1

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

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

Divide each side by '-5'.
z = 0.2

Simplifying
z = 0.2
Subproblem 2
Set the factor '(2 + -1z)' equal to zero and attempt to solve:

Simplifying
2 + -1z = 0

Solving
2 + -1z = 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 + -1z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1z = 0 + -2
-1z = 0 + -2

Combine like terms: 0 + -2 = -2
-1z = -2

Divide each side by '-1'.
z = 2

Simplifying
z = 2
Solution
z = {0.2, 2}