(2x-3)(x)=54

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

Simplifying
(2x + -3)(x) = 54

Reorder the terms:
(-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.
(-9 + -2x)(6 + -1x) = 0

Subproblem 1
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
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 = {-4.5, 6}