-5a^2+10a+75=0

Solution for -5a^2+10a+75=0 equation:

Simplifying
-5a2 + 10a + 75 = 0

Reorder the terms:
75 + 10a + -5a2 = 0

Solving
75 + 10a + -5a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '5'.
5(15 + 2a + -1a2) = 0

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

Ignore the factor 5.
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 '(3 + a)' equal to zero and attempt to solve:

Simplifying
3 + a = 0

Solving
3 + a = 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 + a = 0 + -3

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

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

Simplifying
a = -3
Solution
a = {5, -3}