(u-3)(u+5)=(u+4)(u-1)+(u-1)(u+5)

Solution for (u-3)(u+5)=(u+4)(u-1)+(u-1)(u+5) equation:

Simplifying
(u + -3)(u + 5) = (u + 4)(u + -1) + (u + -1)(u + 5)

Reorder the terms:
(-3 + u)(u + 5) = (u + 4)(u + -1) + (u + -1)(u + 5)

Reorder the terms:
(-3 + u)(5 + u) = (u + 4)(u + -1) + (u + -1)(u + 5)

Multiply (-3 + u) * (5 + u)
(-3(5 + u) + u(5 + u)) = (u + 4)(u + -1) + (u + -1)(u + 5)
((5 * -3 + u * -3) + u(5 + u)) = (u + 4)(u + -1) + (u + -1)(u + 5)
((-15 + -3u) + u(5 + u)) = (u + 4)(u + -1) + (u + -1)(u + 5)
(-15 + -3u + (5 * u + u * u)) = (u + 4)(u + -1) + (u + -1)(u + 5)
(-15 + -3u + (5u + u2)) = (u + 4)(u + -1) + (u + -1)(u + 5)

Combine like terms: -3u + 5u = 2u
(-15 + 2u + u2) = (u + 4)(u + -1) + (u + -1)(u + 5)

Reorder the terms:
-15 + 2u + u2 = (4 + u)(u + -1) + (u + -1)(u + 5)

Reorder the terms:
-15 + 2u + u2 = (4 + u)(-1 + u) + (u + -1)(u + 5)

Multiply (4 + u) * (-1 + u)
-15 + 2u + u2 = (4(-1 + u) + u(-1 + u)) + (u + -1)(u + 5)
-15 + 2u + u2 = ((-1 * 4 + u * 4) + u(-1 + u)) + (u + -1)(u + 5)
-15 + 2u + u2 = ((-4 + 4u) + u(-1 + u)) + (u + -1)(u + 5)
-15 + 2u + u2 = (-4 + 4u + (-1 * u + u * u)) + (u + -1)(u + 5)
-15 + 2u + u2 = (-4 + 4u + (-1u + u2)) + (u + -1)(u + 5)

Combine like terms: 4u + -1u = 3u
-15 + 2u + u2 = (-4 + 3u + u2) + (u + -1)(u + 5)

Reorder the terms:
-15 + 2u + u2 = -4 + 3u + u2 + (-1 + u)(u + 5)

Reorder the terms:
-15 + 2u + u2 = -4 + 3u + u2 + (-1 + u)(5 + u)

Multiply (-1 + u) * (5 + u)
-15 + 2u + u2 = -4 + 3u + u2 + (-1(5 + u) + u(5 + u))
-15 + 2u + u2 = -4 + 3u + u2 + ((5 * -1 + u * -1) + u(5 + u))
-15 + 2u + u2 = -4 + 3u + u2 + ((-5 + -1u) + u(5 + u))
-15 + 2u + u2 = -4 + 3u + u2 + (-5 + -1u + (5 * u + u * u))
-15 + 2u + u2 = -4 + 3u + u2 + (-5 + -1u + (5u + u2))

Combine like terms: -1u + 5u = 4u
-15 + 2u + u2 = -4 + 3u + u2 + (-5 + 4u + u2)

Reorder the terms:
-15 + 2u + u2 = -4 + -5 + 3u + 4u + u2 + u2

Combine like terms: -4 + -5 = -9
-15 + 2u + u2 = -9 + 3u + 4u + u2 + u2

Combine like terms: 3u + 4u = 7u
-15 + 2u + u2 = -9 + 7u + u2 + u2

Combine like terms: u2 + u2 = 2u2
-15 + 2u + u2 = -9 + 7u + 2u2

Solving
-15 + 2u + u2 = -9 + 7u + 2u2

Solving for variable 'u'.

Reorder the terms:
-15 + 9 + 2u + -7u + u2 + -2u2 = -9 + 7u + 2u2 + 9 + -7u + -2u2

Combine like terms: -15 + 9 = -6
-6 + 2u + -7u + u2 + -2u2 = -9 + 7u + 2u2 + 9 + -7u + -2u2

Combine like terms: 2u + -7u = -5u
-6 + -5u + u2 + -2u2 = -9 + 7u + 2u2 + 9 + -7u + -2u2

Combine like terms: u2 + -2u2 = -1u2
-6 + -5u + -1u2 = -9 + 7u + 2u2 + 9 + -7u + -2u2

Reorder the terms:
-6 + -5u + -1u2 = -9 + 9 + 7u + -7u + 2u2 + -2u2

Combine like terms: -9 + 9 = 0
-6 + -5u + -1u2 = 0 + 7u + -7u + 2u2 + -2u2
-6 + -5u + -1u2 = 7u + -7u + 2u2 + -2u2

Combine like terms: 7u + -7u = 0
-6 + -5u + -1u2 = 0 + 2u2 + -2u2
-6 + -5u + -1u2 = 2u2 + -2u2

Combine like terms: 2u2 + -2u2 = 0
-6 + -5u + -1u2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 5u + u2) = 0

Factor a trinomial.
-1((3 + u)(2 + u)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(3 + u)' equal to zero and attempt to solve:

Simplifying
3 + u = 0

Solving
3 + u = 0

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

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

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

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

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

Simplifying
2 + u = 0

Solving
2 + u = 0

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

Add '-2' to each side of the equation.
2 + -2 + u = 0 + -2

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

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

Simplifying
u = -2
Solution
u = {-3, -2}