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

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

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

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

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

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

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