0=6x^2+48x-54

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

Simplifying
0 = 6x2 + 48x + -54

Reorder the terms:
0 = -54 + 48x + 6x2

Solving
0 = -54 + 48x + 6x2

Solving for variable 'x'.

Combine like terms: 0 + 54 = 54
54 + -48x + -6x2 = -54 + 48x + 6x2 + 54 + -48x + -6x2

Reorder the terms:
54 + -48x + -6x2 = -54 + 54 + 48x + -48x + 6x2 + -6x2

Combine like terms: -54 + 54 = 0
54 + -48x + -6x2 = 0 + 48x + -48x + 6x2 + -6x2
54 + -48x + -6x2 = 48x + -48x + 6x2 + -6x2

Combine like terms: 48x + -48x = 0
54 + -48x + -6x2 = 0 + 6x2 + -6x2
54 + -48x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
54 + -48x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(9 + -8x + -1x2) = 0

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

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

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

Simplifying
9 + x = 0

Solving
9 + x = 0

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

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

Combine like terms: 9 + -9 = 0
0 + x = 0 + -9
x = 0 + -9

Combine like terms: 0 + -9 = -9
x = -9

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