(108x^2)-258x+102=0

Solution for (108x^2)-258x+102=0 equation:

Simplifying
(108x2) + -258x + 102 = 0

Reorder the terms:
102 + -258x + (108x2) = 0

Solving
102 + -258x + (108x2) = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(17 + -43x + (18x2)) = 0

Factor a trinomial.
6((1 + -2x)(17 + -9x)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Subproblem 2
Set the factor '(17 + -9x)' equal to zero and attempt to solve:

Simplifying
17 + -9x = 0

Solving
17 + -9x = 0

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

Add '-17' to each side of the equation.
17 + -17 + -9x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -9x = 0 + -17
-9x = 0 + -17

Combine like terms: 0 + -17 = -17
-9x = -17

Divide each side by '-9'.
x = 1.888888889

Simplifying
x = 1.888888889
Solution
x = {0.5, 1.888888889}