-x^2+21x+46=0

Solution for -x^2+21x+46=0 equation:

Simplifying
-1x2 + 21x + 46 = 0

Reorder the terms:
46 + 21x + -1x2 = 0

Solving
46 + 21x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(23 + -1x)(2 + x) = 0

Subproblem 1
Set the factor '(23 + -1x)' equal to zero and attempt to solve:

Simplifying
23 + -1x = 0

Solving
23 + -1x = 0

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

Add '-23' to each side of the equation.
23 + -23 + -1x = 0 + -23

Combine like terms: 23 + -23 = 0
0 + -1x = 0 + -23
-1x = 0 + -23

Combine like terms: 0 + -23 = -23
-1x = -23

Divide each side by '-1'.
x = 23

Simplifying
x = 23
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {23, -2}