3-x=x^2-27

Solution for 3-x=x^2-27 equation:

Simplifying
3 + -1x = x2 + -27

Reorder the terms:
3 + -1x = -27 + x2

Solving
3 + -1x = -27 + x2

Solving for variable 'x'.

Reorder the terms:
3 + 27 + -1x + -1x2 = -27 + x2 + 27 + -1x2

Combine like terms: 3 + 27 = 30
30 + -1x + -1x2 = -27 + x2 + 27 + -1x2

Reorder the terms:
30 + -1x + -1x2 = -27 + 27 + x2 + -1x2

Combine like terms: -27 + 27 = 0
30 + -1x + -1x2 = 0 + x2 + -1x2
30 + -1x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
30 + -1x + -1x2 = 0

Factor a trinomial.
(5 + -1x)(6 + x) = 0

Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Solution
x = {5, -6}