-x^2-2x+6=7

Solution for -x^2-2x+6=7 equation:

Simplifying
-1x2 + -2x + 6 = 7

Reorder the terms:
6 + -2x + -1x2 = 7

Solving
6 + -2x + -1x2 = 7

Solving for variable 'x'.

Reorder the terms:
6 + -7 + -2x + -1x2 = 7 + -7

Combine like terms: 6 + -7 = -1
-1 + -2x + -1x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-1 + -2x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 2x + x2) = 0

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

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

Simplifying
1 + x = 0

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

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

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

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

Simplifying
1 + x = 0

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

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

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

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