2x^2+19x-108=0

Solution for 2x^2+19x-108=0 equation:

Simplifying
2x2 + 19x + -108 = 0

Reorder the terms:
-108 + 19x + 2x2 = 0

Solving
-108 + 19x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-27 + -2x)(4 + -1x) = 0

Subproblem 1
Set the factor '(-27 + -2x)' equal to zero and attempt to solve:

Simplifying
-27 + -2x = 0

Solving
-27 + -2x = 0

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

Add '27' to each side of the equation.
-27 + 27 + -2x = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -2x = 0 + 27
-2x = 0 + 27

Combine like terms: 0 + 27 = 27
-2x = 27

Divide each side by '-2'.
x = -13.5

Simplifying
x = -13.5
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-13.5, 4}