4x^2-41x+102=0

Solution for 4x^2-41x+102=0 equation:

Simplifying
4x2 + -41x + 102 = 0

Reorder the terms:
102 + -41x + 4x2 = 0

Solving
102 + -41x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(17 + -4x)(6 + -1x) = 0

Subproblem 1
Set the factor '(17 + -4x)' equal to zero and attempt to solve:

Simplifying
17 + -4x = 0

Solving
17 + -4x = 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 + -4x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -4x = 0 + -17
-4x = 0 + -17

Combine like terms: 0 + -17 = -17
-4x = -17

Divide each side by '-4'.
x = 4.25

Simplifying
x = 4.25
Subproblem 2
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
Solution
x = {4.25, 6}