30a^2+am-m^2=0

Solution for 30a^2+am-m^2=0 equation:

Simplifying
30a2 + am + -1m2 = 0

Reorder the terms:
am + 30a2 + -1m2 = 0

Solving
am + 30a2 + -1m2 = 0

Solving for variable 'a'.

Factor a trinomial.
(6a + -1m)(5a + m) = 0

Subproblem 1
Set the factor '(6a + -1m)' equal to zero and attempt to solve:

Simplifying
6a + -1m = 0

Solving
6a + -1m = 0

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

Add 'm' to each side of the equation.
6a + -1m + m = 0 + m

Combine like terms: -1m + m = 0
6a + 0 = 0 + m
6a = 0 + m
Remove the zero:
6a = m

Divide each side by '6'.
a = 0.1666666667m

Simplifying
a = 0.1666666667m
Subproblem 2
Set the factor '(5a + m)' equal to zero and attempt to solve:

Simplifying
5a + m = 0

Solving
5a + m = 0

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

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

Combine like terms: m + -1m = 0
5a + 0 = 0 + -1m
5a = 0 + -1m
Remove the zero:
5a = -1m

Divide each side by '5'.
a = -0.2m

Simplifying
a = -0.2m
Solution
a = {0.1666666667m, -0.2m}