-21=2m^2+17m

Solution for -21=2m^2+17m equation:

Simplifying
-21 = 2m2 + 17m

Reorder the terms:
-21 = 17m + 2m2

Solving
-21 = 17m + 2m2

Solving for variable 'm'.

Reorder the terms:
-21 + -17m + -2m2 = 17m + -17m + 2m2 + -2m2

Combine like terms: 17m + -17m = 0
-21 + -17m + -2m2 = 0 + 2m2 + -2m2
-21 + -17m + -2m2 = 2m2 + -2m2

Combine like terms: 2m2 + -2m2 = 0
-21 + -17m + -2m2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(21 + 17m + 2m2) = 0

Factor a trinomial.
-1((7 + m)(3 + 2m)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(7 + m)' equal to zero and attempt to solve:

Simplifying
7 + m = 0

Solving
7 + m = 0

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

Add '-7' to each side of the equation.
7 + -7 + m = 0 + -7

Combine like terms: 7 + -7 = 0
0 + m = 0 + -7
m = 0 + -7

Combine like terms: 0 + -7 = -7
m = -7

Simplifying
m = -7
Subproblem 2
Set the factor '(3 + 2m)' equal to zero and attempt to solve:

Simplifying
3 + 2m = 0

Solving
3 + 2m = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2m = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2m = 0 + -3
2m = 0 + -3

Combine like terms: 0 + -3 = -3
2m = -3

Divide each side by '2'.
m = -1.5

Simplifying
m = -1.5
Solution
m = {-7, -1.5}