2x^2-5x-33=0

Solution for 2x^2-5x-33=0 equation:

Simplifying
2x2 + -5x + -33 = 0

Reorder the terms:
-33 + -5x + 2x2 = 0

Solving
-33 + -5x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-3 + -1x)(11 + -2x) = 0

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 '(11 + -2x)' equal to zero and attempt to solve:

Simplifying
11 + -2x = 0

Solving
11 + -2x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -2x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -2x = 0 + -11
-2x = 0 + -11

Combine like terms: 0 + -11 = -11
-2x = -11

Divide each side by '-2'.
x = 5.5

Simplifying
x = 5.5
Solution
x = {-3, 5.5}