0=-x^2-14x+32

Solution for 0=-x^2-14x+32 equation:

Simplifying
0 = -1x2 + -14x + 32

Reorder the terms:
0 = 32 + -14x + -1x2

Solving
0 = 32 + -14x + -1x2

Solving for variable 'x'.

Combine like terms: 0 + -32 = -32
-32 + 14x + x2 = 32 + -14x + -1x2 + -32 + 14x + x2

Reorder the terms:
-32 + 14x + x2 = 32 + -32 + -14x + 14x + -1x2 + x2

Combine like terms: 32 + -32 = 0
-32 + 14x + x2 = 0 + -14x + 14x + -1x2 + x2
-32 + 14x + x2 = -14x + 14x + -1x2 + x2

Combine like terms: -14x + 14x = 0
-32 + 14x + x2 = 0 + -1x2 + x2
-32 + 14x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-32 + 14x + x2 = 0

Factor a trinomial.
(-16 + -1x)(2 + -1x) = 0

Subproblem 1
Set the factor '(-16 + -1x)' equal to zero and attempt to solve:

Simplifying
-16 + -1x = 0

Solving
-16 + -1x = 0

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

Add '16' to each side of the equation.
-16 + 16 + -1x = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1x = 0 + 16
-1x = 0 + 16

Combine like terms: 0 + 16 = 16
-1x = 16

Divide each side by '-1'.
x = -16

Simplifying
x = -16
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 = {-16, 2}