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

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

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

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

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

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

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

Remove parenthesis around (1 + x)
3 + 2x + -1x2 = 1 + x

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

Solving for variable 'x'.

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

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

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

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

Combine like terms: 1 + -1 = 0
2 + 1x + -1x2 = 0 + x + -1x
2 + 1x + -1x2 = x + -1x

Combine like terms: x + -1x = 0
2 + 1x + -1x2 = 0

Factor a trinomial.
(2 + -1x)(1 + x) = 0

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {2, -1}