16x^2-54x+18=0

Solution for 16x^2-54x+18=0 equation:

Simplifying
16x2 + -54x + 18 = 0

Reorder the terms:
18 + -54x + 16x2 = 0

Solving
18 + -54x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + -27x + 8x2) = 0

Factor a trinomial.
2((3 + -8x)(3 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -8x)' equal to zero and attempt to solve:

Simplifying
3 + -8x = 0

Solving
3 + -8x = 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 + -8x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -8x = 0 + -3
-8x = 0 + -3

Combine like terms: 0 + -3 = -3
-8x = -3

Divide each side by '-8'.
x = 0.375

Simplifying
x = 0.375
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 = {0.375, 3}