x^2=65-8x

Solution for x^2=65-8x equation:

Simplifying
x2 = 65 + -8x

Solving
x2 = 65 + -8x

Solving for variable 'x'.

Reorder the terms:
-65 + 8x + x2 = 65 + -8x + -65 + 8x

Reorder the terms:
-65 + 8x + x2 = 65 + -65 + -8x + 8x

Combine like terms: 65 + -65 = 0
-65 + 8x + x2 = 0 + -8x + 8x
-65 + 8x + x2 = -8x + 8x

Combine like terms: -8x + 8x = 0
-65 + 8x + x2 = 0

Factor a trinomial.
(-13 + -1x)(5 + -1x) = 0

Subproblem 1
Set the factor '(-13 + -1x)' equal to zero and attempt to solve:

Simplifying
-13 + -1x = 0

Solving
-13 + -1x = 0

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

Add '13' to each side of the equation.
-13 + 13 + -1x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -1x = 0 + 13
-1x = 0 + 13

Combine like terms: 0 + 13 = 13
-1x = 13

Divide each side by '-1'.
x = -13

Simplifying
x = -13
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 = {-13, 5}