7x+16=x^2+x

Solution for 7x+16=x^2+x equation:

Simplifying
7x + 16 = x2 + x

Reorder the terms:
16 + 7x = x2 + x

Reorder the terms:
16 + 7x = x + x2

Solving
16 + 7x = x + x2

Solving for variable 'x'.

Combine like terms: 7x + -1x = 6x
16 + 6x + -1x2 = x + x2 + -1x + -1x2

Reorder the terms:
16 + 6x + -1x2 = x + -1x + x2 + -1x2

Combine like terms: x + -1x = 0
16 + 6x + -1x2 = 0 + x2 + -1x2
16 + 6x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
16 + 6x + -1x2 = 0

Factor a trinomial.
(8 + -1x)(2 + x) = 0

Subproblem 1
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

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

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

Divide each side by '-1'.
x = 8

Simplifying
x = 8
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 = {8, -2}