-14m^2+86m+84=0

Solution for -14m^2+86m+84=0 equation:

Simplifying
-14m2 + 86m + 84 = 0

Reorder the terms:
84 + 86m + -14m2 = 0

Solving
84 + 86m + -14m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(42 + 43m + -7m2) = 0

Factor a trinomial.
2((7 + -1m)(6 + 7m)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(7 + -1m)' equal to zero and attempt to solve:

Simplifying
7 + -1m = 0

Solving
7 + -1m = 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 + -1m = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1m = 0 + -7
-1m = 0 + -7

Combine like terms: 0 + -7 = -7
-1m = -7

Divide each side by '-1'.
m = 7

Simplifying
m = 7
Subproblem 2
Set the factor '(6 + 7m)' equal to zero and attempt to solve:

Simplifying
6 + 7m = 0

Solving
6 + 7m = 0

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

Add '-6' to each side of the equation.
6 + -6 + 7m = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 7m = 0 + -6
7m = 0 + -6

Combine like terms: 0 + -6 = -6
7m = -6

Divide each side by '7'.
m = -0.8571428571

Simplifying
m = -0.8571428571
Solution
m = {7, -0.8571428571}