0=x^2-13x+42

Solution for 0=x^2-13x+42 equation:

Simplifying
0 = x2 + -13x + 42

Reorder the terms:
0 = 42 + -13x + x2

Solving
0 = 42 + -13x + x2

Solving for variable 'x'.

Combine like terms: 0 + -42 = -42
-42 + 13x + -1x2 = 42 + -13x + x2 + -42 + 13x + -1x2

Reorder the terms:
-42 + 13x + -1x2 = 42 + -42 + -13x + 13x + x2 + -1x2

Combine like terms: 42 + -42 = 0
-42 + 13x + -1x2 = 0 + -13x + 13x + x2 + -1x2
-42 + 13x + -1x2 = -13x + 13x + x2 + -1x2

Combine like terms: -13x + 13x = 0
-42 + 13x + -1x2 = 0 + x2 + -1x2
-42 + 13x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-42 + 13x + -1x2 = 0

Factor a trinomial.
(-7 + x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-7 + x)' equal to zero and attempt to solve:

Simplifying
-7 + x = 0

Solving
-7 + x = 0

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

Add '7' to each side of the equation.
-7 + 7 + x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + x = 0 + 7
x = 0 + 7

Combine like terms: 0 + 7 = 7
x = 7

Simplifying
x = 7
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

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

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

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {7, 6}