2x^2+50x-108=0

Solution for 2x^2+50x-108=0 equation:

Simplifying
2x2 + 50x + -108 = 0

Reorder the terms:
-108 + 50x + 2x2 = 0

Solving
-108 + 50x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-54 + 25x + x2) = 0

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

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

Simplifying
-27 + -1x = 0

Solving
-27 + -1x = 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 + -1x = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -1x = 0 + 27
-1x = 0 + 27

Combine like terms: 0 + 27 = 27
-1x = 27

Divide each side by '-1'.
x = -27

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-27, 2}