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

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

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

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

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

Multiply (-1 + X) * (3 + X)
(-1(3 + X) + X(3 + X)) = 32
((3 * -1 + X * -1) + X(3 + X)) = 32
((-3 + -1X) + X(3 + X)) = 32
(-3 + -1X + (3 * X + X * X)) = 32
(-3 + -1X + (3X + X2)) = 32

Combine like terms: -1X + 3X = 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}