x^2+429=47x+9

Solution for x^2+429=47x+9 equation:

Simplifying
x2 + 429 = 47x + 9

Reorder the terms:
429 + x2 = 47x + 9

Reorder the terms:
429 + x2 = 9 + 47x

Solving
429 + x2 = 9 + 47x

Solving for variable 'x'.

Reorder the terms:
429 + -9 + -47x + x2 = 9 + 47x + -9 + -47x

Combine like terms: 429 + -9 = 420
420 + -47x + x2 = 9 + 47x + -9 + -47x

Reorder the terms:
420 + -47x + x2 = 9 + -9 + 47x + -47x

Combine like terms: 9 + -9 = 0
420 + -47x + x2 = 0 + 47x + -47x
420 + -47x + x2 = 47x + -47x

Combine like terms: 47x + -47x = 0
420 + -47x + x2 = 0

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}