4U(U-3)=-6-U

Solution for 4U(U-3)=-6-U equation:

Simplifying
4U(U + -3) = -6 + -1U

Reorder the terms:
4U(-3 + U) = -6 + -1U
(-3 * 4U + U * 4U) = -6 + -1U
(-12U + 4U2) = -6 + -1U

Solving
-12U + 4U2 = -6 + -1U

Solving for variable 'U'.

Reorder the terms:
6 + -12U + U + 4U2 = -6 + -1U + 6 + U

Combine like terms: -12U + U = -11U
6 + -11U + 4U2 = -6 + -1U + 6 + U

Reorder the terms:
6 + -11U + 4U2 = -6 + 6 + -1U + U

Combine like terms: -6 + 6 = 0
6 + -11U + 4U2 = 0 + -1U + U
6 + -11U + 4U2 = -1U + U

Combine like terms: -1U + U = 0
6 + -11U + 4U2 = 0

Factor a trinomial.
(3 + -4U)(2 + -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 '(2 + -1U)' equal to zero and attempt to solve:

Simplifying
2 + -1U = 0

Solving
2 + -1U = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1U = 0 + -2

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

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

Divide each side by '-1'.
U = 2

Simplifying
U = 2
Solution
U = {0.75, 2}