(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.
(-7 + -1x)(5 + -1x) = 0

Subproblem 1
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
Subproblem 2
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
Solution
x = {-7, 5}