x^2-55x+156=0

Solution for x^2-55x+156=0 equation:

Simplifying
x2 + -55x + 156 = 0

Reorder the terms:
156 + -55x + x2 = 0

Solving
156 + -55x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + -1x)(52 + -1x) = 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 '(52 + -1x)' equal to zero and attempt to solve:

Simplifying
52 + -1x = 0

Solving
52 + -1x = 0

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

Add '-52' to each side of the equation.
52 + -52 + -1x = 0 + -52

Combine like terms: 52 + -52 = 0
0 + -1x = 0 + -52
-1x = 0 + -52

Combine like terms: 0 + -52 = -52
-1x = -52

Divide each side by '-1'.
x = 52

Simplifying
x = 52
Solution
x = {3, 52}