X*X+4=X+6

Solution for X*X+4=X+6 equation:

Simplifying
X * X + 4 = X + 6

Multiply X * X
X2 + 4 = X + 6

Reorder the terms:
4 + X2 = X + 6

Reorder the terms:
4 + X2 = 6 + X

Solving
4 + X2 = 6 + X

Solving for variable 'X'.

Reorder the terms:
4 + -6 + -1X + X2 = 6 + X + -6 + -1X

Combine like terms: 4 + -6 = -2
-2 + -1X + X2 = 6 + X + -6 + -1X

Reorder the terms:
-2 + -1X + X2 = 6 + -6 + X + -1X

Combine like terms: 6 + -6 = 0
-2 + -1X + X2 = 0 + X + -1X
-2 + -1X + X2 = X + -1X

Combine like terms: X + -1X = 0
-2 + -1X + X2 = 0

Factor a trinomial.
(-1 + -1X)(2 + -1X) = 0

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

Simplifying
-1 + -1X = 0

Solving
-1 + -1X = 0

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

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

Combine like terms: -1 + 1 = 0
0 + -1X = 0 + 1
-1X = 0 + 1

Combine like terms: 0 + 1 = 1
-1X = 1

Divide each side by '-1'.
X = -1

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

Simplifying
2 + -1X = 0

Solving
2 + -1X = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1X = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1X = 0 + -2
-1X = 0 + -2

Combine like terms: 0 + -2 = -2
-1X = -2

Divide each side by '-1'.
X = 2

Simplifying
X = 2
Solution
X = {-1, 2}