47-2x=x^2+32

Solution for 47-2x=x^2+32 equation:

Simplifying
47 + -2x = x2 + 32

Reorder the terms:
47 + -2x = 32 + x2

Solving
47 + -2x = 32 + x2

Solving for variable 'x'.

Reorder the terms:
47 + -32 + -2x + -1x2 = 32 + x2 + -32 + -1x2

Combine like terms: 47 + -32 = 15
15 + -2x + -1x2 = 32 + x2 + -32 + -1x2

Reorder the terms:
15 + -2x + -1x2 = 32 + -32 + x2 + -1x2

Combine like terms: 32 + -32 = 0
15 + -2x + -1x2 = 0 + x2 + -1x2
15 + -2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
15 + -2x + -1x2 = 0

Factor a trinomial.
(3 + -1x)(5 + x) = 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 '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Solution
x = {3, -5}