(x-3)(x+1)=32

Solution for (x-3)(x+1)=32 equation:

Simplifying
(x + -3)(x + 1) = 32

Reorder the terms:
(-3 + x)(x + 1) = 32

Reorder the terms:
(-3 + x)(1 + x) = 32

Multiply (-3 + x) * (1 + x)
(-3(1 + x) + x(1 + x)) = 32
((1 * -3 + x * -3) + x(1 + x)) = 32
((-3 + -3x) + x(1 + x)) = 32
(-3 + -3x + (1 * x + x * x)) = 32
(-3 + -3x + (1x + x2)) = 32

Combine like terms: -3x + 1x = -2x
(-3 + -2x + x2) = 32

Solving
-3 + -2x + x2 = 32

Solving for variable 'x'.

Reorder the terms:
-3 + -32 + -2x + x2 = 32 + -32

Combine like terms: -3 + -32 = -35
-35 + -2x + x2 = 32 + -32

Combine like terms: 32 + -32 = 0
-35 + -2x + x2 = 0

Factor a trinomial.
(-5 + -1x)(7 + -1x) = 0

Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5
Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-5, 7}