m(2m+9)=5

Solution for m(2m+9)=5 equation:

Simplifying
m(2m + 9) = 5

Reorder the terms:
m(9 + 2m) = 5
(9 * m + 2m * m) = 5
(9m + 2m2) = 5

Solving
9m + 2m2 = 5

Solving for variable 'm'.

Reorder the terms:
-5 + 9m + 2m2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 9m + 2m2 = 0

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

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

Simplifying
-5 + -1m = 0

Solving
-5 + -1m = 0

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

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

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

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

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

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

Simplifying
1 + -2m = 0

Solving
1 + -2m = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2m = 0 + -1

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

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

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

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