(4u-2)(1+u)=0

Solution for (4u-2)(1+u)=0 equation:

Simplifying
(4u + -2)(1 + u) = 0

Reorder the terms:
(-2 + 4u)(1 + u) = 0

Multiply (-2 + 4u) * (1 + u)
(-2(1 + u) + 4u * (1 + u)) = 0
((1 * -2 + u * -2) + 4u * (1 + u)) = 0
((-2 + -2u) + 4u * (1 + u)) = 0
(-2 + -2u + (1 * 4u + u * 4u)) = 0
(-2 + -2u + (4u + 4u2)) = 0

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

Solving
-2 + 2u + 4u2 = 0

Solving for variable 'u'.

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

Factor a trinomial.
2((-1 + -1u)(1 + -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 '(1 + -2u)' equal to zero and attempt to solve:

Simplifying
1 + -2u = 0

Solving
1 + -2u = 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 + -2u = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2u = 0 + -1
-2u = 0 + -1

Combine like terms: 0 + -1 = -1
-2u = -1

Divide each side by '-2'.
u = 0.5

Simplifying
u = 0.5
Solution
u = {-1, 0.5}