65=x^2-18x+130

Solution for 65=x^2-18x+130 equation:

Simplifying
65 = x2 + -18x + 130

Reorder the terms:
65 = 130 + -18x + x2

Solving
65 = 130 + -18x + x2

Solving for variable 'x'.

Combine like terms: 65 + -130 = -65
-65 + 18x + -1x2 = 130 + -18x + x2 + -130 + 18x + -1x2

Reorder the terms:
-65 + 18x + -1x2 = 130 + -130 + -18x + 18x + x2 + -1x2

Combine like terms: 130 + -130 = 0
-65 + 18x + -1x2 = 0 + -18x + 18x + x2 + -1x2
-65 + 18x + -1x2 = -18x + 18x + x2 + -1x2

Combine like terms: -18x + 18x = 0
-65 + 18x + -1x2 = 0 + x2 + -1x2
-65 + 18x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-65 + 18x + -1x2 = 0

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

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

Simplifying
-13 + x = 0

Solving
-13 + x = 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 + x = 0 + 13

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

Combine like terms: 0 + 13 = 13
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}