-x^2-2x+3=-21

Solution for -x^2-2x+3=-21 equation:

Simplifying
-1x2 + -2x + 3 = -21

Reorder the terms:
3 + -2x + -1x2 = -21

Solving
3 + -2x + -1x2 = -21

Solving for variable 'x'.

Reorder the terms:
3 + 21 + -2x + -1x2 = -21 + 21

Combine like terms: 3 + 21 = 24
24 + -2x + -1x2 = -21 + 21

Combine like terms: -21 + 21 = 0
24 + -2x + -1x2 = 0

Factor a trinomial.
(4 + -1x)(6 + x) = 0

Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Solution
x = {4, -6}