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

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

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

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

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

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

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

Reorder the terms:
-3 + -2x + x2 = 1 + x

Solving
-3 + -2x + x2 = 1 + x

Solving for variable 'x'.

Reorder the terms:
-3 + -1 + -2x + -1x + x2 = 1 + x + -1 + -1x

Combine like terms: -3 + -1 = -4
-4 + -2x + -1x + x2 = 1 + x + -1 + -1x

Combine like terms: -2x + -1x = -3x
-4 + -3x + x2 = 1 + x + -1 + -1x

Reorder the terms:
-4 + -3x + x2 = 1 + -1 + x + -1x

Combine like terms: 1 + -1 = 0
-4 + -3x + x2 = 0 + x + -1x
-4 + -3x + x2 = x + -1x

Combine like terms: x + -1x = 0
-4 + -3x + x2 = 0

Factor a trinomial.
(-1 + -1x)(4 + -1x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-1, 4}