X*X-42=X

Solution for X*X-42=X equation:

Simplifying
X * X + -42 = X

Multiply X * X
X2 + -42 = X

Reorder the terms:
-42 + X2 = X

Solving
-42 + X2 = X

Solving for variable 'X'.

Reorder the terms:
-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}