(3+2x)x=54

Solution for (3+2x)x=54 equation:

Simplifying
(3 + 2x) * x = 54

Reorder the terms for easier multiplication:
x(3 + 2x) = 54
(3 * x + 2x * x) = 54
(3x + 2x2) = 54

Solving
3x + 2x2 = 54

Solving for variable 'x'.

Reorder the terms:
-54 + 3x + 2x2 = 54 + -54

Combine like terms: 54 + -54 = 0
-54 + 3x + 2x2 = 0

Factor a trinomial.
(-6 + -1x)(9 + -2x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(9 + -2x)' equal to zero and attempt to solve:

Simplifying
9 + -2x = 0

Solving
9 + -2x = 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 + -2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2x = 0 + -9
-2x = 0 + -9

Combine like terms: 0 + -9 = -9
-2x = -9

Divide each side by '-2'.
x = 4.5

Simplifying
x = 4.5
Solution
x = {-6, 4.5}