54x^2+x-123=0

Solution for 54x^2+x-123=0 equation:

Simplifying
54x2 + x + -123 = 0

Reorder the terms:
-123 + x + 54x2 = 0

Solving
-123 + x + 54x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-41 + -27x)(3 + -2x) = 0

Subproblem 1
Set the factor '(-41 + -27x)' equal to zero and attempt to solve:

Simplifying
-41 + -27x = 0

Solving
-41 + -27x = 0

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

Add '41' to each side of the equation.
-41 + 41 + -27x = 0 + 41

Combine like terms: -41 + 41 = 0
0 + -27x = 0 + 41
-27x = 0 + 41

Combine like terms: 0 + 41 = 41
-27x = 41

Divide each side by '-27'.
x = -1.518518519

Simplifying
x = -1.518518519
Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

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

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

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-1.518518519, 1.5}