0=2x^2+33x-54

Solution for 0=2x^2+33x-54 equation:

Simplifying
0 = 2x2 + 33x + -54

Reorder the terms:
0 = -54 + 33x + 2x2

Solving
0 = -54 + 33x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + 54 = 54
54 + -33x + -2x2 = -54 + 33x + 2x2 + 54 + -33x + -2x2

Reorder the terms:
54 + -33x + -2x2 = -54 + 54 + 33x + -33x + 2x2 + -2x2

Combine like terms: -54 + 54 = 0
54 + -33x + -2x2 = 0 + 33x + -33x + 2x2 + -2x2
54 + -33x + -2x2 = 33x + -33x + 2x2 + -2x2

Combine like terms: 33x + -33x = 0
54 + -33x + -2x2 = 0 + 2x2 + -2x2
54 + -33x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
54 + -33x + -2x2 = 0

Factor a trinomial.
(3 + -2x)(18 + x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(18 + x)' equal to zero and attempt to solve:

Simplifying
18 + x = 0

Solving
18 + x = 0

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

Add '-18' to each side of the equation.
18 + -18 + x = 0 + -18

Combine like terms: 18 + -18 = 0
0 + x = 0 + -18
x = 0 + -18

Combine like terms: 0 + -18 = -18
x = -18

Simplifying
x = -18
Solution
x = {1.5, -18}