9x-8=6+x^2

Solution for 9x-8=6+x^2 equation:

Simplifying
9x + -8 = 6 + x2

Reorder the terms:
-8 + 9x = 6 + x2

Solving
-8 + 9x = 6 + x2

Solving for variable 'x'.

Reorder the terms:
-8 + -6 + 9x + -1x2 = 6 + x2 + -6 + -1x2

Combine like terms: -8 + -6 = -14
-14 + 9x + -1x2 = 6 + x2 + -6 + -1x2

Reorder the terms:
-14 + 9x + -1x2 = 6 + -6 + x2 + -1x2

Combine like terms: 6 + -6 = 0
-14 + 9x + -1x2 = 0 + x2 + -1x2
-14 + 9x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-14 + 9x + -1x2 = 0

Factor a trinomial.
(-7 + x)(2 + -1x) = 0

Subproblem 1
Set the factor '(-7 + x)' equal to zero and attempt to solve:

Simplifying
-7 + x = 0

Solving
-7 + x = 0

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

Add '7' to each side of the equation.
-7 + 7 + x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + x = 0 + 7
x = 0 + 7

Combine like terms: 0 + 7 = 7
x = 7

Simplifying
x = 7
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 = {7, 2}