4=x^2-6x+13

Solution for 4=x^2-6x+13 equation:

Simplifying
4 = x2 + -6x + 13

Reorder the terms:
4 = 13 + -6x + x2

Solving
4 = 13 + -6x + x2

Solving for variable 'x'.

Combine like terms: 4 + -13 = -9
-9 + 6x + -1x2 = 13 + -6x + x2 + -13 + 6x + -1x2

Reorder the terms:
-9 + 6x + -1x2 = 13 + -13 + -6x + 6x + x2 + -1x2

Combine like terms: 13 + -13 = 0
-9 + 6x + -1x2 = 0 + -6x + 6x + x2 + -1x2
-9 + 6x + -1x2 = -6x + 6x + x2 + -1x2

Combine like terms: -6x + 6x = 0
-9 + 6x + -1x2 = 0 + x2 + -1x2
-9 + 6x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-9 + 6x + -1x2 = 0

Factor a trinomial.
(-3 + x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-3 + x)' equal to zero and attempt to solve:

Simplifying
-3 + x = 0

Solving
-3 + x = 0

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

Add '3' to each side of the equation.
-3 + 3 + x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + x = 0 + 3
x = 0 + 3

Combine like terms: 0 + 3 = 3
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {3, 3}