4x^2-53x+165=0

Solution for 4x^2-53x+165=0 equation:

Simplifying
4x2 + -53x + 165 = 0

Reorder the terms:
165 + -53x + 4x2 = 0

Solving
165 + -53x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5 + -1x)(33 + -4x) = 0

Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Subproblem 2
Set the factor '(33 + -4x)' equal to zero and attempt to solve:

Simplifying
33 + -4x = 0

Solving
33 + -4x = 0

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

Add '-33' to each side of the equation.
33 + -33 + -4x = 0 + -33

Combine like terms: 33 + -33 = 0
0 + -4x = 0 + -33
-4x = 0 + -33

Combine like terms: 0 + -33 = -33
-4x = -33

Divide each side by '-4'.
x = 8.25

Simplifying
x = 8.25
Solution
x = {5, 8.25}