(u+1)(u-4)=0

Solution for (u+1)(u-4)=0 equation:

Simplifying
(u + 1)(u + -4) = 0

Reorder the terms:
(1 + u)(u + -4) = 0

Reorder the terms:
(1 + u)(-4 + u) = 0

Multiply (1 + u) * (-4 + u)
(1(-4 + u) + u(-4 + u)) = 0
((-4 * 1 + u * 1) + u(-4 + u)) = 0
((-4 + 1u) + u(-4 + u)) = 0
(-4 + 1u + (-4 * u + u * u)) = 0
(-4 + 1u + (-4u + u2)) = 0

Combine like terms: 1u + -4u = -3u
(-4 + -3u + u2) = 0

Solving
-4 + -3u + u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-1 + -1u)(4 + -1u) = 0

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

Simplifying
-1 + -1u = 0

Solving
-1 + -1u = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1u = 0 + 1

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

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

Divide each side by '-1'.
u = -1

Simplifying
u = -1
Subproblem 2
Set the factor '(4 + -1u)' equal to zero and attempt to solve:

Simplifying
4 + -1u = 0

Solving
4 + -1u = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1u = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1u = 0 + -4
-1u = 0 + -4

Combine like terms: 0 + -4 = -4
-1u = -4

Divide each side by '-1'.
u = 4

Simplifying
u = 4
Solution
u = {-1, 4}