-x^2-3x+5=1

Solution for -x^2-3x+5=1 equation:

Simplifying
-1x2 + -3x + 5 = 1

Reorder the terms:
5 + -3x + -1x2 = 1

Solving
5 + -3x + -1x2 = 1

Solving for variable 'x'.

Reorder the terms:
5 + -1 + -3x + -1x2 = 1 + -1

Combine like terms: 5 + -1 = 4
4 + -3x + -1x2 = 1 + -1

Combine like terms: 1 + -1 = 0
4 + -3x + -1x2 = 0

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

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 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 + x = 0 + -4

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

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

Simplifying
x = -4
Solution
x = {1, -4}