11x^2-209x+374=0

Solution for 11x^2-209x+374=0 equation:

Simplifying
11x2 + -209x + 374 = 0

Reorder the terms:
374 + -209x + 11x2 = 0

Solving
374 + -209x + 11x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '11'.
11(34 + -19x + x2) = 0

Factor a trinomial.
11((2 + -1x)(17 + -1x)) = 0

Ignore the factor 11.
Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Subproblem 2
Set the factor '(17 + -1x)' equal to zero and attempt to solve:

Simplifying
17 + -1x = 0

Solving
17 + -1x = 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 + -1x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -1x = 0 + -17
-1x = 0 + -17

Combine like terms: 0 + -17 = -17
-1x = -17

Divide each side by '-1'.
x = 17

Simplifying
x = 17
Solution
x = {2, 17}