0=16a^2-8a-3

Solution for 0=16a^2-8a-3 equation:

Simplifying
0 = 16a2 + -8a + -3

Reorder the terms:
0 = -3 + -8a + 16a2

Solving
0 = -3 + -8a + 16a2

Solving for variable 'a'.

Combine like terms: 0 + 3 = 3
3 + 8a + -16a2 = -3 + -8a + 16a2 + 3 + 8a + -16a2

Reorder the terms:
3 + 8a + -16a2 = -3 + 3 + -8a + 8a + 16a2 + -16a2

Combine like terms: -3 + 3 = 0
3 + 8a + -16a2 = 0 + -8a + 8a + 16a2 + -16a2
3 + 8a + -16a2 = -8a + 8a + 16a2 + -16a2

Combine like terms: -8a + 8a = 0
3 + 8a + -16a2 = 0 + 16a2 + -16a2
3 + 8a + -16a2 = 16a2 + -16a2

Combine like terms: 16a2 + -16a2 = 0
3 + 8a + -16a2 = 0

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

Subproblem 1
Set the factor '(3 + -4a)' equal to zero and attempt to solve:

Simplifying
3 + -4a = 0

Solving
3 + -4a = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4a = 0 + -3
-4a = 0 + -3

Combine like terms: 0 + -3 = -3
-4a = -3

Divide each side by '-4'.
a = 0.75

Simplifying
a = 0.75
Subproblem 2
Set the factor '(1 + 4a)' equal to zero and attempt to solve:

Simplifying
1 + 4a = 0

Solving
1 + 4a = 0

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

Add '-1' to each side of the equation.
1 + -1 + 4a = 0 + -1

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

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

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

Simplifying
a = -0.25
Solution
a = {0.75, -0.25}