2x^2-43x+111=0

Solution for 2x^2-43x+111=0 equation:

Simplifying
2x2 + -43x + 111 = 0

Reorder the terms:
111 + -43x + 2x2 = 0

Solving
111 + -43x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + -1x)(37 + -2x) = 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 '(37 + -2x)' equal to zero and attempt to solve:

Simplifying
37 + -2x = 0

Solving
37 + -2x = 0

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

Add '-37' to each side of the equation.
37 + -37 + -2x = 0 + -37

Combine like terms: 37 + -37 = 0
0 + -2x = 0 + -37
-2x = 0 + -37

Combine like terms: 0 + -37 = -37
-2x = -37

Divide each side by '-2'.
x = 18.5

Simplifying
x = 18.5
Solution
x = {3, 18.5}