3(x+1)-x(x-1)=x+5

Solution for 3(x+1)-x(x-1)=x+5 equation:

Simplifying
3(x + 1) + -1x(x + -1) = x + 5

Reorder the terms:
3(1 + x) + -1x(x + -1) = x + 5
(1 * 3 + x * 3) + -1x(x + -1) = x + 5
(3 + 3x) + -1x(x + -1) = x + 5

Reorder the terms:
3 + 3x + -1x(-1 + x) = x + 5
3 + 3x + (-1 * -1x + x * -1x) = x + 5
3 + 3x + (1x + -1x2) = x + 5

Combine like terms: 3x + 1x = 4x
3 + 4x + -1x2 = x + 5

Reorder the terms:
3 + 4x + -1x2 = 5 + x

Solving
3 + 4x + -1x2 = 5 + x

Solving for variable 'x'.

Reorder the terms:
3 + -5 + 4x + -1x + -1x2 = 5 + x + -5 + -1x

Combine like terms: 3 + -5 = -2
-2 + 4x + -1x + -1x2 = 5 + x + -5 + -1x

Combine like terms: 4x + -1x = 3x
-2 + 3x + -1x2 = 5 + x + -5 + -1x

Reorder the terms:
-2 + 3x + -1x2 = 5 + -5 + x + -1x

Combine like terms: 5 + -5 = 0
-2 + 3x + -1x2 = 0 + x + -1x
-2 + 3x + -1x2 = x + -1x

Combine like terms: x + -1x = 0
-2 + 3x + -1x2 = 0

Factor a trinomial.
(-2 + x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-2 + x)' equal to zero and attempt to solve:

Simplifying
-2 + x = 0

Solving
-2 + x = 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 + x = 0 + 2

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

Combine like terms: 0 + 2 = 2
x = 2

Simplifying
x = 2
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 = {2, 1}