5a^2-10a-84=-9

Solution for 5a^2-10a-84=-9 equation:

Simplifying
5a2 + -10a + -84 = -9

Reorder the terms:
-84 + -10a + 5a2 = -9

Solving
-84 + -10a + 5a2 = -9

Solving for variable 'a'.

Reorder the terms:
-84 + 9 + -10a + 5a2 = -9 + 9

Combine like terms: -84 + 9 = -75
-75 + -10a + 5a2 = -9 + 9

Combine like terms: -9 + 9 = 0
-75 + -10a + 5a2 = 0

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

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

Ignore the factor 5.
Subproblem 1
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
Subproblem 2
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
Solution
a = {-3, 5}