0=-2x^2+23x+39

Solution for 0=-2x^2+23x+39 equation:

Simplifying
0 = -2x2 + 23x + 39

Reorder the terms:
0 = 39 + 23x + -2x2

Solving
0 = 39 + 23x + -2x2

Solving for variable 'x'.

Combine like terms: 0 + -39 = -39
-39 + -23x + 2x2 = 39 + 23x + -2x2 + -39 + -23x + 2x2

Reorder the terms:
-39 + -23x + 2x2 = 39 + -39 + 23x + -23x + -2x2 + 2x2

Combine like terms: 39 + -39 = 0
-39 + -23x + 2x2 = 0 + 23x + -23x + -2x2 + 2x2
-39 + -23x + 2x2 = 23x + -23x + -2x2 + 2x2

Combine like terms: 23x + -23x = 0
-39 + -23x + 2x2 = 0 + -2x2 + 2x2
-39 + -23x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-39 + -23x + 2x2 = 0

Factor a trinomial.
(-3 + -2x)(13 + -1x) = 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 '(13 + -1x)' equal to zero and attempt to solve:

Simplifying
13 + -1x = 0

Solving
13 + -1x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1x = 0 + -13
-1x = 0 + -13

Combine like terms: 0 + -13 = -13
-1x = -13

Divide each side by '-1'.
x = 13

Simplifying
x = 13
Solution
x = {-1.5, 13}