0=473+54x+x^2

Solution for 0=473+54x+x^2 equation:

Simplifying
0 = 473 + 54x + x2

Solving
0 = 473 + 54x + x2

Solving for variable 'x'.

Combine like terms: 0 + -473 = -473
-473 + -54x + -1x2 = 473 + 54x + x2 + -473 + -54x + -1x2

Reorder the terms:
-473 + -54x + -1x2 = 473 + -473 + 54x + -54x + x2 + -1x2

Combine like terms: 473 + -473 = 0
-473 + -54x + -1x2 = 0 + 54x + -54x + x2 + -1x2
-473 + -54x + -1x2 = 54x + -54x + x2 + -1x2

Combine like terms: 54x + -54x = 0
-473 + -54x + -1x2 = 0 + x2 + -1x2
-473 + -54x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-473 + -54x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(473 + 54x + x2) = 0

Factor a trinomial.
-1((43 + x)(11 + x)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(43 + x)' equal to zero and attempt to solve:

Simplifying
43 + x = 0

Solving
43 + x = 0

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

Add '-43' to each side of the equation.
43 + -43 + x = 0 + -43

Combine like terms: 43 + -43 = 0
0 + x = 0 + -43
x = 0 + -43

Combine like terms: 0 + -43 = -43
x = -43

Simplifying
x = -43
Subproblem 2
Set the factor '(11 + x)' equal to zero and attempt to solve:

Simplifying
11 + x = 0

Solving
11 + x = 0

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

Add '-11' to each side of the equation.
11 + -11 + x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + x = 0 + -11
x = 0 + -11

Combine like terms: 0 + -11 = -11
x = -11

Simplifying
x = -11
Solution
x = {-43, -11}