2x^2-24x=-54

Solution for 2x^2-24x=-54 equation:

Simplifying
2x2 + -24x = -54

Reorder the terms:
-24x + 2x2 = -54

Solving
-24x + 2x2 = -54

Solving for variable 'x'.

Reorder the terms:
54 + -24x + 2x2 = -54 + 54

Combine like terms: -54 + 54 = 0
54 + -24x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(27 + -12x + x2) = 0

Factor a trinomial.
2((3 + -1x)(9 + -1x)) = 0

Ignore the factor 2.
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 '(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
Solution
x = {3, 9}