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

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

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

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

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

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

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