-x^2+6x-1=x+3

Solution for -x^2+6x-1=x+3 equation:

Simplifying
-1x2 + 6x + -1 = x + 3

Reorder the terms:
-1 + 6x + -1x2 = x + 3

Reorder the terms:
-1 + 6x + -1x2 = 3 + x

Solving
-1 + 6x + -1x2 = 3 + x

Solving for variable 'x'.

Reorder the terms:
-1 + -3 + 6x + -1x + -1x2 = 3 + x + -3 + -1x

Combine like terms: -1 + -3 = -4
-4 + 6x + -1x + -1x2 = 3 + x + -3 + -1x

Combine like terms: 6x + -1x = 5x
-4 + 5x + -1x2 = 3 + x + -3 + -1x

Reorder the terms:
-4 + 5x + -1x2 = 3 + -3 + x + -1x

Combine like terms: 3 + -3 = 0
-4 + 5x + -1x2 = 0 + x + -1x
-4 + 5x + -1x2 = x + -1x

Combine like terms: x + -1x = 0
-4 + 5x + -1x2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
x = {4, 1}