X*X+23X=624

Solution for X*X+23X=624 equation:

Simplifying
X * X + 23X = 624

Multiply X * X
X2 + 23X = 624

Reorder the terms:
23X + X2 = 624

Solving
23X + X2 = 624

Solving for variable 'X'.

Reorder the terms:
-624 + 23X + X2 = 624 + -624

Combine like terms: 624 + -624 = 0
-624 + 23X + X2 = 0

Factor a trinomial.
(-39 + -1X)(16 + -1X) = 0

Subproblem 1
Set the factor '(-39 + -1X)' equal to zero and attempt to solve:

Simplifying
-39 + -1X = 0

Solving
-39 + -1X = 0

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

Add '39' to each side of the equation.
-39 + 39 + -1X = 0 + 39

Combine like terms: -39 + 39 = 0
0 + -1X = 0 + 39
-1X = 0 + 39

Combine like terms: 0 + 39 = 39
-1X = 39

Divide each side by '-1'.
X = -39

Simplifying
X = -39
Subproblem 2
Set the factor '(16 + -1X)' equal to zero and attempt to solve:

Simplifying
16 + -1X = 0

Solving
16 + -1X = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1X = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1X = 0 + -16
-1X = 0 + -16

Combine like terms: 0 + -16 = -16
-1X = -16

Divide each side by '-1'.
X = 16

Simplifying
X = 16
Solution
X = {-39, 16}