x^2=x+42

Solution for x^2=x+42 equation:

Simplifying
x2 = x + 42

Reorder the terms:
x2 = 42 + x

Solving
x2 = 42 + x

Solving for variable 'x'.

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

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

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

Combine like terms: x + -1x = 0
-42 + -1x + 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}