x^2-52x+147=0

Solution for x^2-52x+147=0 equation:

Simplifying
x2 + -52x + 147 = 0

Reorder the terms:
147 + -52x + x2 = 0

Solving
147 + -52x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + -1x)(49 + -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 '(49 + -1x)' equal to zero and attempt to solve:

Simplifying
49 + -1x = 0

Solving
49 + -1x = 0

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

Add '-49' to each side of the equation.
49 + -49 + -1x = 0 + -49

Combine like terms: 49 + -49 = 0
0 + -1x = 0 + -49
-1x = 0 + -49

Combine like terms: 0 + -49 = -49
-1x = -49

Divide each side by '-1'.
x = 49

Simplifying
x = 49
Solution
x = {3, 49}