6a^2-30a-84=0

Solution for 6a^2-30a-84=0 equation:

Simplifying
6a2 + -30a + -84 = 0

Reorder the terms:
-84 + -30a + 6a2 = 0

Solving
-84 + -30a + 6a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-14 + -5a + a2) = 0

Factor a trinomial.
6((-2 + -1a)(7 + -1a)) = 0

Ignore the factor 6.
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 '(7 + -1a)' equal to zero and attempt to solve:

Simplifying
7 + -1a = 0

Solving
7 + -1a = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1a = 0 + -7
-1a = 0 + -7

Combine like terms: 0 + -7 = -7
-1a = -7

Divide each side by '-1'.
a = 7

Simplifying
a = 7
Solution
a = {-2, 7}