x=-x^2+6

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

Simplifying
x = -1x2 + 6

Reorder the terms:
x = 6 + -1x2

Solving
x = 6 + -1x2

Solving for variable 'x'.

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

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

Combine like terms: 6 + -6 = 0
-6 + x + x2 = 0 + -1x2 + x2
-6 + x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-6 + x + x2 = 0

Factor a trinomial.
(-3 + -1x)(2 + -1x) = 0

Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

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

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

Divide each side by '-1'.
x = -3

Simplifying
x = -3
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-3, 2}