X^2-14X=-33

Solution for X^2-14X=-33 equation:

Simplifying
X2 + -14X = -33

Reorder the terms:
-14X + X2 = -33

Solving
-14X + X2 = -33

Solving for variable 'X'.

Reorder the terms:
33 + -14X + X2 = -33 + 33

Combine like terms: -33 + 33 = 0
33 + -14X + X2 = 0

Factor a trinomial.
(3 + -1X)(11 + -1X) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(11 + -1X)' equal to zero and attempt to solve:

Simplifying
11 + -1X = 0

Solving
11 + -1X = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1X = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1X = 0 + -11
-1X = 0 + -11

Combine like terms: 0 + -11 = -11
-1X = -11

Divide each side by '-1'.
X = 11

Simplifying
X = 11
Solution
X = {3, 11}