300=-4a^2+80a

Solution for 300=-4a^2+80a equation:

Simplifying
300 = -4a2 + 80a

Reorder the terms:
300 = 80a + -4a2

Solving
300 = 80a + -4a2

Solving for variable 'a'.

Reorder the terms:
300 + -80a + 4a2 = 80a + -80a + -4a2 + 4a2

Combine like terms: 80a + -80a = 0
300 + -80a + 4a2 = 0 + -4a2 + 4a2
300 + -80a + 4a2 = -4a2 + 4a2

Combine like terms: -4a2 + 4a2 = 0
300 + -80a + 4a2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(75 + -20a + a2) = 0

Factor a trinomial.
4((5 + -1a)(15 + -1a)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(5 + -1a)' equal to zero and attempt to solve:

Simplifying
5 + -1a = 0

Solving
5 + -1a = 0

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

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

Combine like terms: 5 + -5 = 0
0 + -1a = 0 + -5
-1a = 0 + -5

Combine like terms: 0 + -5 = -5
-1a = -5

Divide each side by '-1'.
a = 5

Simplifying
a = 5
Subproblem 2
Set the factor '(15 + -1a)' equal to zero and attempt to solve:

Simplifying
15 + -1a = 0

Solving
15 + -1a = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1a = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1a = 0 + -15
-1a = 0 + -15

Combine like terms: 0 + -15 = -15
-1a = -15

Divide each side by '-1'.
a = 15

Simplifying
a = 15
Solution
a = {5, 15}