2m^2+20m+42=0

Solution for 2m^2+20m+42=0 equation:

Simplifying
2m2 + 20m + 42 = 0

Reorder the terms:
42 + 20m + 2m2 = 0

Solving
42 + 20m + 2m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(21 + 10m + m2) = 0

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

Ignore the factor 2.
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 + m)' equal to zero and attempt to solve:

Simplifying
3 + m = 0

Solving
3 + m = 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 + m = 0 + -3

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

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

Simplifying
m = -3
Solution
m = {-7, -3}