8x=x^2-20

Solution for 8x=x^2-20 equation:

Simplifying
8x = x2 + -20

Reorder the terms:
8x = -20 + x2

Solving
8x = -20 + x2

Solving for variable 'x'.

Reorder the terms:
20 + 8x + -1x2 = -20 + x2 + 20 + -1x2

Reorder the terms:
20 + 8x + -1x2 = -20 + 20 + x2 + -1x2

Combine like terms: -20 + 20 = 0
20 + 8x + -1x2 = 0 + x2 + -1x2
20 + 8x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
20 + 8x + -1x2 = 0

Factor a trinomial.
(10 + -1x)(2 + x) = 0

Subproblem 1
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

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

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

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {10, -2}