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

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

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

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

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

Multiply (-3 + x) * (-2 + x)
1 + x = (-3(-2 + x) + x(-2 + x))
1 + x = ((-2 * -3 + x * -3) + x(-2 + x))
1 + x = ((6 + -3x) + x(-2 + x))
1 + x = (6 + -3x + (-2 * x + x * x))
1 + x = (6 + -3x + (-2x + x2))

Combine like terms: -3x + -2x = -5x
1 + x = (6 + -5x + x2)

Solving
1 + x = 6 + -5x + x2

Solving for variable 'x'.

Reorder the terms:
1 + -6 + x + 5x + -1x2 = 6 + -5x + x2 + -6 + 5x + -1x2

Combine like terms: 1 + -6 = -5
-5 + x + 5x + -1x2 = 6 + -5x + x2 + -6 + 5x + -1x2

Combine like terms: x + 5x = 6x
-5 + 6x + -1x2 = 6 + -5x + x2 + -6 + 5x + -1x2

Reorder the terms:
-5 + 6x + -1x2 = 6 + -6 + -5x + 5x + x2 + -1x2

Combine like terms: 6 + -6 = 0
-5 + 6x + -1x2 = 0 + -5x + 5x + x2 + -1x2
-5 + 6x + -1x2 = -5x + 5x + x2 + -1x2

Combine like terms: -5x + 5x = 0
-5 + 6x + -1x2 = 0 + x2 + -1x2
-5 + 6x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-5 + 6x + -1x2 = 0

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

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

Simplifying
-5 + x = 0

Solving
-5 + x = 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 + x = 0 + 5

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

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

Simplifying
x = 5
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 = {5, 1}