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

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

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

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

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

Multiply (3 + 4u) * (-3 + u)
(3(-3 + u) + 4u * (-3 + u)) = 0
((-3 * 3 + u * 3) + 4u * (-3 + u)) = 0
((-9 + 3u) + 4u * (-3 + u)) = 0
(-9 + 3u + (-3 * 4u + u * 4u)) = 0
(-9 + 3u + (-12u + 4u2)) = 0

Combine like terms: 3u + -12u = -9u
(-9 + -9u + 4u2) = 0

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

Solving for variable 'u'.

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

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

Simplifying
3 + -1u = 0

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

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

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

Divide each side by '-1'.
u = 3

Simplifying
u = 3
Solution
u = {-0.75, 3}