30=25a-5a^2

Solution for 30=25a-5a^2 equation:

Simplifying
30 = 25a + -5a2

Solving
30 = 25a + -5a2

Solving for variable 'a'.

Reorder the terms:
30 + -25a + 5a2 = 25a + -25a + -5a2 + 5a2

Combine like terms: 25a + -25a = 0
30 + -25a + 5a2 = 0 + -5a2 + 5a2
30 + -25a + 5a2 = -5a2 + 5a2

Combine like terms: -5a2 + 5a2 = 0
30 + -25a + 5a2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(6 + -5a + a2) = 0

Factor a trinomial.
5((2 + -1a)(3 + -1a)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(2 + -1a)' equal to zero and attempt to solve:

Simplifying
2 + -1a = 0

Solving
2 + -1a = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1a = 0 + -2
-1a = 0 + -2

Combine like terms: 0 + -2 = -2
-1a = -2

Divide each side by '-1'.
a = 2

Simplifying
a = 2
Subproblem 2
Set the factor '(3 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

Solving
3 + -1a = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1a = 0 + -3
-1a = 0 + -3

Combine like terms: 0 + -3 = -3
-1a = -3

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Solution
a = {2, 3}