x^2=13x-42

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

Simplifying
x2 = 13x + -42

Reorder the terms:
x2 = -42 + 13x

Solving
x2 = -42 + 13x

Solving for variable 'x'.

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

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

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

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

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

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

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

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