3x^2-52x+204=0

Solution for 3x^2-52x+204=0 equation:

Simplifying
3x2 + -52x + 204 = 0

Reorder the terms:
204 + -52x + 3x2 = 0

Solving
204 + -52x + 3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(6 + -1x)(34 + -3x) = 0

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

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Subproblem 2
Set the factor '(34 + -3x)' equal to zero and attempt to solve:

Simplifying
34 + -3x = 0

Solving
34 + -3x = 0

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

Add '-34' to each side of the equation.
34 + -34 + -3x = 0 + -34

Combine like terms: 34 + -34 = 0
0 + -3x = 0 + -34
-3x = 0 + -34

Combine like terms: 0 + -34 = -34
-3x = -34

Divide each side by '-3'.
x = 11.33333333

Simplifying
x = 11.33333333
Solution
x = {6, 11.33333333}