6x^2-37x+57=0

Solution for 6x^2-37x+57=0 equation:

Simplifying
6x2 + -37x + 57 = 0

Reorder the terms:
57 + -37x + 6x2 = 0

Solving
57 + -37x + 6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + -1x)(19 + -6x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(19 + -6x)' equal to zero and attempt to solve:

Simplifying
19 + -6x = 0

Solving
19 + -6x = 0

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

Add '-19' to each side of the equation.
19 + -19 + -6x = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -6x = 0 + -19
-6x = 0 + -19

Combine like terms: 0 + -19 = -19
-6x = -19

Divide each side by '-6'.
x = 3.166666667

Simplifying
x = 3.166666667
Solution
x = {3, 3.166666667}