-x^2-40x+84=0

Solution for -x^2-40x+84=0 equation:

Simplifying
-1x2 + -40x + 84 = 0

Reorder the terms:
84 + -40x + -1x2 = 0

Solving
84 + -40x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2 + -1x)(42 + 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 '(42 + x)' equal to zero and attempt to solve:

Simplifying
42 + x = 0

Solving
42 + x = 0

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

Add '-42' to each side of the equation.
42 + -42 + x = 0 + -42

Combine like terms: 42 + -42 = 0
0 + x = 0 + -42
x = 0 + -42

Combine like terms: 0 + -42 = -42
x = -42

Simplifying
x = -42
Solution
x = {2, -42}