(1+u)(4u-6)=0

Solution for (1+u)(4u-6)=0 equation:

Simplifying
(1 + u)(4u + -6) = 0

Reorder the terms:
(1 + u)(-6 + 4u) = 0

Multiply (1 + u) * (-6 + 4u)
(1(-6 + 4u) + u(-6 + 4u)) = 0
((-6 * 1 + 4u * 1) + u(-6 + 4u)) = 0
((-6 + 4u) + u(-6 + 4u)) = 0
(-6 + 4u + (-6 * u + 4u * u)) = 0
(-6 + 4u + (-6u + 4u2)) = 0

Combine like terms: 4u + -6u = -2u
(-6 + -2u + 4u2) = 0

Solving
-6 + -2u + 4u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -1u + 2u2) = 0

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

Ignore the factor 2.
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 '(3 + -2u)' equal to zero and attempt to solve:

Simplifying
3 + -2u = 0

Solving
3 + -2u = 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 + -2u = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2u = 0 + -3
-2u = 0 + -3

Combine like terms: 0 + -3 = -3
-2u = -3

Divide each side by '-2'.
u = 1.5

Simplifying
u = 1.5
Solution
u = {-1, 1.5}