-4u^2+8u-3=0

Solution for -4u^2+8u-3=0 equation:

Simplifying
-4u2 + 8u + -3 = 0

Reorder the terms:
-3 + 8u + -4u2 = 0

Solving
-3 + 8u + -4u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-3 + 2u)(1 + -2u) = 0

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

Simplifying
-3 + 2u = 0

Solving
-3 + 2u = 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 + 2u = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 2u = 0 + 3
2u = 0 + 3

Combine like terms: 0 + 3 = 3
2u = 3

Divide each side by '2'.
u = 1.5

Simplifying
u = 1.5
Subproblem 2
Set the factor '(1 + -2u)' equal to zero and attempt to solve:

Simplifying
1 + -2u = 0

Solving
1 + -2u = 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 + -2u = 0 + -1

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

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

Divide each side by '-2'.
u = 0.5

Simplifying
u = 0.5
Solution
u = {1.5, 0.5}