-x^2-32x+68=0

Solution for -x^2-32x+68=0 equation:

Simplifying
-1x2 + -32x + 68 = 0

Reorder the terms:
68 + -32x + -1x2 = 0

Solving
68 + -32x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2 + -1x)(34 + x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(34 + x)' equal to zero and attempt to solve:

Simplifying
34 + x = 0

Solving
34 + x = 0

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

Add '-34' to each side of the equation.
34 + -34 + x = 0 + -34

Combine like terms: 34 + -34 = 0
0 + x = 0 + -34
x = 0 + -34

Combine like terms: 0 + -34 = -34
x = -34

Simplifying
x = -34
Solution
x = {2, -34}