4U^2-3=11U

Solution for 4U^2-3=11U equation:

Simplifying
4U2 + -3 = 11U

Reorder the terms:
-3 + 4U2 = 11U

Solving
-3 + 4U2 = 11U

Solving for variable 'U'.

Reorder the terms:
-3 + -11U + 4U2 = 11U + -11U

Combine like terms: 11U + -11U = 0
-3 + -11U + 4U2 = 0

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

Subproblem 1
Set the factor '(-1 + -4U)' equal to zero and attempt to solve:

Simplifying
-1 + -4U = 0

Solving
-1 + -4U = 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 + -4U = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4U = 0 + 1
-4U = 0 + 1

Combine like terms: 0 + 1 = 1
-4U = 1

Divide each side by '-4'.
U = -0.25

Simplifying
U = -0.25
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 = {-0.25, 3}