(6+u)(4u-3)=0

Solution for (6+u)(4u-3)=0 equation:

Simplifying
(6 + u)(4u + -3) = 0

Reorder the terms:
(6 + u)(-3 + 4u) = 0

Multiply (6 + u) * (-3 + 4u)
(6(-3 + 4u) + u(-3 + 4u)) = 0
((-3 * 6 + 4u * 6) + u(-3 + 4u)) = 0
((-18 + 24u) + u(-3 + 4u)) = 0
(-18 + 24u + (-3 * u + 4u * u)) = 0
(-18 + 24u + (-3u + 4u2)) = 0

Combine like terms: 24u + -3u = 21u
(-18 + 21u + 4u2) = 0

Solving
-18 + 21u + 4u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-6 + -1u)(3 + -4u) = 0

Subproblem 1
Set the factor '(-6 + -1u)' equal to zero and attempt to solve:

Simplifying
-6 + -1u = 0

Solving
-6 + -1u = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1u = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1u = 0 + 6
-1u = 0 + 6

Combine like terms: 0 + 6 = 6
-1u = 6

Divide each side by '-1'.
u = -6

Simplifying
u = -6
Subproblem 2
Set the factor '(3 + -4u)' equal to zero and attempt to solve:

Simplifying
3 + -4u = 0

Solving
3 + -4u = 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 + -4u = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4u = 0 + -3
-4u = 0 + -3

Combine like terms: 0 + -3 = -3
-4u = -3

Divide each side by '-4'.
u = 0.75

Simplifying
u = 0.75
Solution
u = {-6, 0.75}