10+7x=-x^2-2-x

Solution for 10+7x=-x^2-2-x equation:

Simplifying
10 + 7x = -1x2 + -2 + -1x

Reorder the terms:
10 + 7x = -2 + -1x + -1x2

Solving
10 + 7x = -2 + -1x + -1x2

Solving for variable 'x'.

Reorder the terms:
10 + 2 + 7x + x + x2 = -2 + -1x + -1x2 + 2 + x + x2

Combine like terms: 10 + 2 = 12
12 + 7x + x + x2 = -2 + -1x + -1x2 + 2 + x + x2

Combine like terms: 7x + x = 8x
12 + 8x + x2 = -2 + -1x + -1x2 + 2 + x + x2

Reorder the terms:
12 + 8x + x2 = -2 + 2 + -1x + x + -1x2 + x2

Combine like terms: -2 + 2 = 0
12 + 8x + x2 = 0 + -1x + x + -1x2 + x2
12 + 8x + x2 = -1x + x + -1x2 + x2

Combine like terms: -1x + x = 0
12 + 8x + x2 = 0 + -1x2 + x2
12 + 8x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
12 + 8x + x2 = 0

Factor a trinomial.
(6 + x)(2 + x) = 0

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

Simplifying
2 + x = 0

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

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

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

Simplifying
x = -2
Solution
x = {-6, -2}