(x-3)2=(x+1)(x-1)-20

Solution for (x-3)2=(x+1)(x-1)-20 equation:

Simplifying
(x + -3) * 2 = (x + 1)(x + -1) + -20

Reorder the terms:
(-3 + x) * 2 = (x + 1)(x + -1) + -20

Reorder the terms for easier multiplication:
2(-3 + x) = (x + 1)(x + -1) + -20
(-3 * 2 + x * 2) = (x + 1)(x + -1) + -20
(-6 + 2x) = (x + 1)(x + -1) + -20

Reorder the terms:
-6 + 2x = (1 + x)(x + -1) + -20

Reorder the terms:
-6 + 2x = (1 + x)(-1 + x) + -20

Multiply (1 + x) * (-1 + x)
-6 + 2x = (1(-1 + x) + x(-1 + x)) + -20
-6 + 2x = ((-1 * 1 + x * 1) + x(-1 + x)) + -20
-6 + 2x = ((-1 + 1x) + x(-1 + x)) + -20
-6 + 2x = (-1 + 1x + (-1 * x + x * x)) + -20
-6 + 2x = (-1 + 1x + (-1x + x2)) + -20

Combine like terms: 1x + -1x = 0
-6 + 2x = (-1 + 0 + x2) + -20
-6 + 2x = (-1 + x2) + -20

Reorder the terms:
-6 + 2x = -1 + -20 + x2

Combine like terms: -1 + -20 = -21
-6 + 2x = -21 + x2

Solving
-6 + 2x = -21 + x2

Solving for variable 'x'.

Reorder the terms:
-6 + 21 + 2x + -1x2 = -21 + x2 + 21 + -1x2

Combine like terms: -6 + 21 = 15
15 + 2x + -1x2 = -21 + x2 + 21 + -1x2

Reorder the terms:
15 + 2x + -1x2 = -21 + 21 + x2 + -1x2

Combine like terms: -21 + 21 = 0
15 + 2x + -1x2 = 0 + x2 + -1x2
15 + 2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
15 + 2x + -1x2 = 0

Factor a trinomial.
(5 + -1x)(3 + x) = 0

Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {5, -3}