54x^2-186x+72=0

Solution for 54x^2-186x+72=0 equation:

Simplifying
54x2 + -186x + 72 = 0

Reorder the terms:
72 + -186x + 54x2 = 0

Solving
72 + -186x + 54x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(12 + -31x + 9x2) = 0

Factor a trinomial.
6((4 + -9x)(3 + -1x)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(4 + -9x)' equal to zero and attempt to solve:

Simplifying
4 + -9x = 0

Solving
4 + -9x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -9x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -9x = 0 + -4
-9x = 0 + -4

Combine like terms: 0 + -4 = -4
-9x = -4

Divide each side by '-9'.
x = 0.4444444444

Simplifying
x = 0.4444444444
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0.4444444444, 3}