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

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

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

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

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

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

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

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

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

Solving for variable 'x'.

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

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

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

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

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

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

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

Subproblem 1
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
Subproblem 2
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
Solution
x = {-4, 1}