x-20=10-x^2

Solution for x-20=10-x^2 equation:

Simplifying
x + -20 = 10 + -1x2

Reorder the terms:
-20 + x = 10 + -1x2

Solving
-20 + x = 10 + -1x2

Solving for variable 'x'.

Reorder the terms:
-20 + -10 + x + x2 = 10 + -1x2 + -10 + x2

Combine like terms: -20 + -10 = -30
-30 + x + x2 = 10 + -1x2 + -10 + x2

Reorder the terms:
-30 + x + x2 = 10 + -10 + -1x2 + x2

Combine like terms: 10 + -10 = 0
-30 + x + x2 = 0 + -1x2 + x2
-30 + x + x2 = -1x2 + x2

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

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

Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 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 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
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
Solution
x = {-6, 5}