2z^2+9z=5

Solution for 2z^2+9z=5 equation:

Simplifying
2z2 + 9z = 5

Reorder the terms:
9z + 2z2 = 5

Solving
9z + 2z2 = 5

Solving for variable 'z'.

Reorder the terms:
-5 + 9z + 2z2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 9z + 2z2 = 0

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

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

Simplifying
1 + -2z = 0

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

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

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

Divide each side by '-2'.
z = 0.5

Simplifying
z = 0.5
Solution
z = {-5, 0.5}