-x^2+32x+9=8x+32

Solution for -x^2+32x+9=8x+32 equation:

Simplifying
-1x2 + 32x + 9 = 8x + 32

Reorder the terms:
9 + 32x + -1x2 = 8x + 32

Reorder the terms:
9 + 32x + -1x2 = 32 + 8x

Solving
9 + 32x + -1x2 = 32 + 8x

Solving for variable 'x'.

Reorder the terms:
9 + -32 + 32x + -8x + -1x2 = 32 + 8x + -32 + -8x

Combine like terms: 9 + -32 = -23
-23 + 32x + -8x + -1x2 = 32 + 8x + -32 + -8x

Combine like terms: 32x + -8x = 24x
-23 + 24x + -1x2 = 32 + 8x + -32 + -8x

Reorder the terms:
-23 + 24x + -1x2 = 32 + -32 + 8x + -8x

Combine like terms: 32 + -32 = 0
-23 + 24x + -1x2 = 0 + 8x + -8x
-23 + 24x + -1x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-23 + 24x + -1x2 = 0

Factor a trinomial.
(-23 + x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-23 + x)' equal to zero and attempt to solve:

Simplifying
-23 + x = 0

Solving
-23 + x = 0

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

Add '23' to each side of the equation.
-23 + 23 + x = 0 + 23

Combine like terms: -23 + 23 = 0
0 + x = 0 + 23
x = 0 + 23

Combine like terms: 0 + 23 = 23
x = 23

Simplifying
x = 23
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {23, 1}