16a^2-16a+1=-2

Solution for 16a^2-16a+1=-2 equation:

Simplifying
16a2 + -16a + 1 = -2

Reorder the terms:
1 + -16a + 16a2 = -2

Solving
1 + -16a + 16a2 = -2

Solving for variable 'a'.

Reorder the terms:
1 + 2 + -16a + 16a2 = -2 + 2

Combine like terms: 1 + 2 = 3
3 + -16a + 16a2 = -2 + 2

Combine like terms: -2 + 2 = 0
3 + -16a + 16a2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
a = {0.25, 0.75}