(1+u)(4u-9)=0

Solution for (1+u)(4u-9)=0 equation:

Simplifying
(1 + u)(4u + -9) = 0

Reorder the terms:
(1 + u)(-9 + 4u) = 0

Multiply (1 + u) * (-9 + 4u)
(1(-9 + 4u) + u(-9 + 4u)) = 0
((-9 * 1 + 4u * 1) + u(-9 + 4u)) = 0
((-9 + 4u) + u(-9 + 4u)) = 0
(-9 + 4u + (-9 * u + 4u * u)) = 0
(-9 + 4u + (-9u + 4u2)) = 0

Combine like terms: 4u + -9u = -5u
(-9 + -5u + 4u2) = 0

Solving
-9 + -5u + 4u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-1 + -1u)(9 + -4u) = 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 '(9 + -4u)' equal to zero and attempt to solve:

Simplifying
9 + -4u = 0

Solving
9 + -4u = 0

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

Add '-9' to each side of the equation.
9 + -9 + -4u = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4u = 0 + -9
-4u = 0 + -9

Combine like terms: 0 + -9 = -9
-4u = -9

Divide each side by '-4'.
u = 2.25

Simplifying
u = 2.25
Solution
u = {-1, 2.25}