-x^2+41x=400

Solution for -x^2+41x=400 equation:

Simplifying
-1x2 + 41x = 400

Reorder the terms:
41x + -1x2 = 400

Solving
41x + -1x2 = 400

Solving for variable 'x'.

Reorder the terms:
-400 + 41x + -1x2 = 400 + -400

Combine like terms: 400 + -400 = 0
-400 + 41x + -1x2 = 0

Factor a trinomial.
(-25 + x)(16 + -1x) = 0

Subproblem 1
Set the factor '(-25 + x)' equal to zero and attempt to solve:

Simplifying
-25 + x = 0

Solving
-25 + x = 0

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

Add '25' to each side of the equation.
-25 + 25 + x = 0 + 25

Combine like terms: -25 + 25 = 0
0 + x = 0 + 25
x = 0 + 25

Combine like terms: 0 + 25 = 25
x = 25

Simplifying
x = 25
Subproblem 2
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
Solution
x = {25, 16}