(X+3)(X)=54

Solution for (X+3)(X)=54 equation:

Simplifying
(X + 3)(X) = 54

Reorder the terms:
(3 + X)(X) = 54

Reorder the terms for easier multiplication:
X(3 + X) = 54
(3 * X + X * X) = 54
(3X + X2) = 54

Solving
3X + X2 = 54

Solving for variable 'X'.

Reorder the terms:
-54 + 3X + X2 = 54 + -54

Combine like terms: 54 + -54 = 0
-54 + 3X + X2 = 0

Factor a trinomial.
(-9 + -1X)(6 + -1X) = 0

Subproblem 1
Set the factor '(-9 + -1X)' equal to zero and attempt to solve:

Simplifying
-9 + -1X = 0

Solving
-9 + -1X = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1X = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1X = 0 + 9
-1X = 0 + 9

Combine like terms: 0 + 9 = 9
-1X = 9

Divide each side by '-1'.
X = -9

Simplifying
X = -9
Subproblem 2
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
Solution
X = {-9, 6}