8U^2-5U-3=0

Solution for 8U^2-5U-3=0 equation:

Simplifying
8U2 + -5U + -3 = 0

Reorder the terms:
-3 + -5U + 8U2 = 0

Solving
-3 + -5U + 8U2 = 0

Solving for variable 'U'.

Factor a trinomial.
(-3 + -8U)(1 + -1U) = 0

Subproblem 1
Set the factor '(-3 + -8U)' equal to zero and attempt to solve:

Simplifying
-3 + -8U = 0

Solving
-3 + -8U = 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 + -8U = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -8U = 0 + 3
-8U = 0 + 3

Combine like terms: 0 + 3 = 3
-8U = 3

Divide each side by '-8'.
U = -0.375

Simplifying
U = -0.375
Subproblem 2
Set the factor '(1 + -1U)' equal to zero and attempt to solve:

Simplifying
1 + -1U = 0

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

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

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

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

Simplifying
U = 1
Solution
U = {-0.375, 1}