x^2-x-32=7x+1

Solution for x^2-x-32=7x+1 equation:

Simplifying
x2 + -1x + -32 = 7x + 1

Reorder the terms:
-32 + -1x + x2 = 7x + 1

Reorder the terms:
-32 + -1x + x2 = 1 + 7x

Solving
-32 + -1x + x2 = 1 + 7x

Solving for variable 'x'.

Reorder the terms:
-32 + -1 + -1x + -7x + x2 = 1 + 7x + -1 + -7x

Combine like terms: -32 + -1 = -33
-33 + -1x + -7x + x2 = 1 + 7x + -1 + -7x

Combine like terms: -1x + -7x = -8x
-33 + -8x + x2 = 1 + 7x + -1 + -7x

Reorder the terms:
-33 + -8x + x2 = 1 + -1 + 7x + -7x

Combine like terms: 1 + -1 = 0
-33 + -8x + x2 = 0 + 7x + -7x
-33 + -8x + x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-33 + -8x + x2 = 0

Factor a trinomial.
(-3 + -1x)(11 + -1x) = 0

Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3
Subproblem 2
Set the factor '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {-3, 11}