x^2-47x+420=0

Solution for x^2-47x+420=0 equation:

Simplifying
x2 + -47x + 420 = 0

Reorder the terms:
420 + -47x + x2 = 0

Solving
420 + -47x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(12 + -1x)(35 + -1x) = 0

Subproblem 1
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Subproblem 2
Set the factor '(35 + -1x)' equal to zero and attempt to solve:

Simplifying
35 + -1x = 0

Solving
35 + -1x = 0

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

Add '-35' to each side of the equation.
35 + -35 + -1x = 0 + -35

Combine like terms: 35 + -35 = 0
0 + -1x = 0 + -35
-1x = 0 + -35

Combine like terms: 0 + -35 = -35
-1x = -35

Divide each side by '-1'.
x = 35

Simplifying
x = 35
Solution
x = {12, 35}