X^2-X-3=3

Solution for X^2-X-3=3 equation:

Simplifying
X2 + -1X + -3 = 3

Reorder the terms:
-3 + -1X + X2 = 3

Solving
-3 + -1X + X2 = 3

Solving for variable 'X'.

Reorder the terms:
-3 + -3 + -1X + X2 = 3 + -3

Combine like terms: -3 + -3 = -6
-6 + -1X + X2 = 3 + -3

Combine like terms: 3 + -3 = 0
-6 + -1X + X2 = 0

Factor a trinomial.
(-2 + -1X)(3 + -1X) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(3 + -1X)' equal to zero and attempt to solve:

Simplifying
3 + -1X = 0

Solving
3 + -1X = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1X = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1X = 0 + -3
-1X = 0 + -3

Combine like terms: 0 + -3 = -3
-1X = -3

Divide each side by '-1'.
X = 3

Simplifying
X = 3
Solution
X = {-2, 3}