20m^2=-30m-10

Solution for 20m^2=-30m-10 equation:

Simplifying
20m2 = -30m + -10

Reorder the terms:
20m2 = -10 + -30m

Solving
20m2 = -10 + -30m

Solving for variable 'm'.

Reorder the terms:
10 + 30m + 20m2 = -10 + -30m + 10 + 30m

Reorder the terms:
10 + 30m + 20m2 = -10 + 10 + -30m + 30m

Combine like terms: -10 + 10 = 0
10 + 30m + 20m2 = 0 + -30m + 30m
10 + 30m + 20m2 = -30m + 30m

Combine like terms: -30m + 30m = 0
10 + 30m + 20m2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(1 + 3m + 2m2) = 0

Factor a trinomial.
10((1 + m)(1 + 2m)) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(1 + m)' equal to zero and attempt to solve:

Simplifying
1 + m = 0

Solving
1 + m = 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 + m = 0 + -1

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

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

Simplifying
m = -1
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 = {-1, -0.5}