(2u+3)(3u-1)=0

Solution for (2u+3)(3u-1)=0 equation:

Simplifying
(2u + 3)(3u + -1) = 0

Reorder the terms:
(3 + 2u)(3u + -1) = 0

Reorder the terms:
(3 + 2u)(-1 + 3u) = 0

Multiply (3 + 2u) * (-1 + 3u)
(3(-1 + 3u) + 2u * (-1 + 3u)) = 0
((-1 * 3 + 3u * 3) + 2u * (-1 + 3u)) = 0
((-3 + 9u) + 2u * (-1 + 3u)) = 0
(-3 + 9u + (-1 * 2u + 3u * 2u)) = 0
(-3 + 9u + (-2u + 6u2)) = 0

Combine like terms: 9u + -2u = 7u
(-3 + 7u + 6u2) = 0

Solving
-3 + 7u + 6u2 = 0

Solving for variable 'u'.

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

Subproblem 1
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
Subproblem 2
Set the factor '(1 + -3u)' equal to zero and attempt to solve:

Simplifying
1 + -3u = 0

Solving
1 + -3u = 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 + -3u = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3u = 0 + -1
-3u = 0 + -1

Combine like terms: 0 + -1 = -1
-3u = -1

Divide each side by '-3'.
u = 0.3333333333

Simplifying
u = 0.3333333333
Solution
u = {-1.5, 0.3333333333}