6a^2-28a-48=0

Solution for 6a^2-28a-48=0 equation:

Simplifying
6a2 + -28a + -48 = 0

Reorder the terms:
-48 + -28a + 6a2 = 0

Solving
-48 + -28a + 6a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-24 + -14a + 3a2) = 0

Factor a trinomial.
2((-4 + -3a)(6 + -1a)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + -3a)' equal to zero and attempt to solve:

Simplifying
-4 + -3a = 0

Solving
-4 + -3a = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3a = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3a = 0 + 4
-3a = 0 + 4

Combine like terms: 0 + 4 = 4
-3a = 4

Divide each side by '-3'.
a = -1.333333333

Simplifying
a = -1.333333333
Subproblem 2
Set the factor '(6 + -1a)' equal to zero and attempt to solve:

Simplifying
6 + -1a = 0

Solving
6 + -1a = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1a = 0 + -6
-1a = 0 + -6

Combine like terms: 0 + -6 = -6
-1a = -6

Divide each side by '-1'.
a = 6

Simplifying
a = 6
Solution
a = {-1.333333333, 6}