(u-3)(u+1)=u

Solution for (u-3)(u+1)=u equation:

Simplifying
(u + -3)(u + 1) = u

Reorder the terms:
(-3 + u)(u + 1) = u

Reorder the terms:
(-3 + u)(1 + u) = u

Multiply (-3 + u) * (1 + u)
(-3(1 + u) + u(1 + u)) = u
((1 * -3 + u * -3) + u(1 + u)) = u
((-3 + -3u) + u(1 + u)) = u
(-3 + -3u + (1 * u + u * u)) = u
(-3 + -3u + (1u + u2)) = u

Combine like terms: -3u + 1u = -2u
(-3 + -2u + u2) = u

Solving
-3 + -2u + u2 = u

Solving for variable 'u'.

Reorder the terms:
-3 + -2u + -1u + u2 = u + -1u

Combine like terms: -2u + -1u = -3u
-3 + -3u + u2 = u + -1u

Combine like terms: u + -1u = 0
-3 + -3u + u2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -3u + 3 + u2 = 0 + 3

Reorder the terms:
-3 + 3 + -3u + u2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -3u + u2 = 0 + 3
-3u + u2 = 0 + 3

Combine like terms: 0 + 3 = 3
-3u + u2 = 3

The u term is -3u.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3u + 2.25 + u2 = 3 + 2.25

Reorder the terms:
2.25 + -3u + u2 = 3 + 2.25

Combine like terms: 3 + 2.25 = 5.25
2.25 + -3u + u2 = 5.25

Factor a perfect square on the left side:
(u + -1.5)(u + -1.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(u + -1.5) equal to 2.291287847 and -2.291287847.

Subproblem 1
u + -1.5 = 2.291287847

Simplifying
u + -1.5 = 2.291287847

Reorder the terms:
-1.5 + u = 2.291287847

Solving
-1.5 + u = 2.291287847

Solving for variable 'u'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + u = 2.291287847 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + u = 2.291287847 + 1.5
u = 2.291287847 + 1.5

Combine like terms: 2.291287847 + 1.5 = 3.791287847
u = 3.791287847

Simplifying
u = 3.791287847

Subproblem 2
u + -1.5 = -2.291287847

Simplifying
u + -1.5 = -2.291287847

Reorder the terms:
-1.5 + u = -2.291287847

Solving
-1.5 + u = -2.291287847

Solving for variable 'u'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + u = -2.291287847 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + u = -2.291287847 + 1.5
u = -2.291287847 + 1.5

Combine like terms: -2.291287847 + 1.5 = -0.791287847
u = -0.791287847

Simplifying
u = -0.791287847

Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {3.791287847, -0.791287847}