4x-x-1=x(x+1)

Solution for 4x-x-1=x(x+1) equation:

Simplifying
4x + -1x + -1 = x(x + 1)

Reorder the terms:
-1 + 4x + -1x = x(x + 1)

Combine like terms: 4x + -1x = 3x
-1 + 3x = x(x + 1)

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

Solving
-1 + 3x = 1x + x2

Solving for variable 'x'.

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

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

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

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

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

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

Simplifying
-1 + x = 0

Solving
-1 + x = 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 + x = 0 + 1

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

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

Simplifying
x = 1
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 = {1, 1}