40=2z^2+11z

Solution for 40=2z^2+11z equation:

Simplifying
40 = 2z2 + 11z

Reorder the terms:
40 = 11z + 2z2

Solving
40 = 11z + 2z2

Solving for variable 'z'.

Reorder the terms:
40 + -11z + -2z2 = 11z + -11z + 2z2 + -2z2

Combine like terms: 11z + -11z = 0
40 + -11z + -2z2 = 0 + 2z2 + -2z2
40 + -11z + -2z2 = 2z2 + -2z2

Combine like terms: 2z2 + -2z2 = 0
40 + -11z + -2z2 = 0

Factor a trinomial.
(5 + -2z)(8 + z) = 0

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

Simplifying
5 + -2z = 0

Solving
5 + -2z = 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 + -2z = 0 + -5

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

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

Divide each side by '-2'.
z = 2.5

Simplifying
z = 2.5
Subproblem 2
Set the factor '(8 + z)' equal to zero and attempt to solve:

Simplifying
8 + z = 0

Solving
8 + z = 0

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

Add '-8' to each side of the equation.
8 + -8 + z = 0 + -8

Combine like terms: 8 + -8 = 0
0 + z = 0 + -8
z = 0 + -8

Combine like terms: 0 + -8 = -8
z = -8

Simplifying
z = -8
Solution
z = {2.5, -8}