0=x^2-13x+36

Solution for 0=x^2-13x+36 equation:

Simplifying
0 = x2 + -13x + 36

Reorder the terms:
0 = 36 + -13x + x2

Solving
0 = 36 + -13x + x2

Solving for variable 'x'.

Combine like terms: 0 + -36 = -36
-36 + 13x + -1x2 = 36 + -13x + x2 + -36 + 13x + -1x2

Reorder the terms:
-36 + 13x + -1x2 = 36 + -36 + -13x + 13x + x2 + -1x2

Combine like terms: 36 + -36 = 0
-36 + 13x + -1x2 = 0 + -13x + 13x + x2 + -1x2
-36 + 13x + -1x2 = -13x + 13x + x2 + -1x2

Combine like terms: -13x + 13x = 0
-36 + 13x + -1x2 = 0 + x2 + -1x2
-36 + 13x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-36 + 13x + -1x2 = 0

Factor a trinomial.
(-9 + x)(4 + -1x) = 0

Subproblem 1
Set the factor '(-9 + x)' equal to zero and attempt to solve:

Simplifying
-9 + x = 0

Solving
-9 + x = 0

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

Add '9' to each side of the equation.
-9 + 9 + x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + x = 0 + 9
x = 0 + 9

Combine like terms: 0 + 9 = 9
x = 9

Simplifying
x = 9
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {9, 4}