2x^2-41x+74=0

Solution for 2x^2-41x+74=0 equation:

Simplifying
2x2 + -41x + 74 = 0

Reorder the terms:
74 + -41x + 2x2 = 0

Solving
74 + -41x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2 + -1x)(37 + -2x) = 0

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 '(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 = {2, 18.5}