(2x-3)(x+1)=x^2-1

Solution for (2x-3)(x+1)=x^2-1 equation:

Simplifying
(2x + -3)(x + 1) = x2 + -1

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

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

Multiply (-3 + 2x) * (1 + x)
(-3(1 + x) + 2x * (1 + x)) = x2 + -1
((1 * -3 + x * -3) + 2x * (1 + x)) = x2 + -1
((-3 + -3x) + 2x * (1 + x)) = x2 + -1
(-3 + -3x + (1 * 2x + x * 2x)) = x2 + -1
(-3 + -3x + (2x + 2x2)) = x2 + -1

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

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

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

Solving for variable 'x'.

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

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

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

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

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

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

Factor a trinomial.
(-1 + -1x)(2 + -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 '(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
Solution
x = {-1, 2}