-x^2+42x-80=0

Solution for -x^2+42x-80=0 equation:

Simplifying
-1x2 + 42x + -80 = 0

Reorder the terms:
-80 + 42x + -1x2 = 0

Solving
-80 + 42x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-40 + x)(2 + -1x) = 0

Subproblem 1
Set the factor '(-40 + x)' equal to zero and attempt to solve:

Simplifying
-40 + x = 0

Solving
-40 + x = 0

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

Add '40' to each side of the equation.
-40 + 40 + x = 0 + 40

Combine like terms: -40 + 40 = 0
0 + x = 0 + 40
x = 0 + 40

Combine like terms: 0 + 40 = 40
x = 40

Simplifying
x = 40
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 = {40, 2}