48X^2-108X+54=0

Solution for 48X^2-108X+54=0 equation:

Simplifying
48X2 + -108X + 54 = 0

Reorder the terms:
54 + -108X + 48X2 = 0

Solving
54 + -108X + 48X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '6'.
6(9 + -18X + 8X2) = 0

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

Ignore the factor 6.
Subproblem 1
Set the factor '(3 + -4X)' equal to zero and attempt to solve:

Simplifying
3 + -4X = 0

Solving
3 + -4X = 0

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

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

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

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

Divide each side by '-4'.
X = 0.75

Simplifying
X = 0.75
Subproblem 2
Set the factor '(3 + -2X)' equal to zero and attempt to solve:

Simplifying
3 + -2X = 0

Solving
3 + -2X = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2X = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2X = 0 + -3
-2X = 0 + -3

Combine like terms: 0 + -3 = -3
-2X = -3

Divide each side by '-2'.
X = 1.5

Simplifying
X = 1.5
Solution
X = {0.75, 1.5}