6a^2+48a-54=0

Solution for 6a^2+48a-54=0 equation:

Simplifying
6a2 + 48a + -54 = 0

Reorder the terms:
-54 + 48a + 6a2 = 0

Solving
-54 + 48a + 6a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-9 + 8a + a2) = 0

Factor a trinomial.
6((-9 + -1a)(1 + -1a)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-9 + -1a)' equal to zero and attempt to solve:

Simplifying
-9 + -1a = 0

Solving
-9 + -1a = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1a = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1a = 0 + 9
-1a = 0 + 9

Combine like terms: 0 + 9 = 9
-1a = 9

Divide each side by '-1'.
a = -9

Simplifying
a = -9
Subproblem 2
Set the factor '(1 + -1a)' equal to zero and attempt to solve:

Simplifying
1 + -1a = 0

Solving
1 + -1a = 0

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

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

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

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

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

Simplifying
a = 1
Solution
a = {-9, 1}