16z^2+3=16z

Solution for 16z^2+3=16z equation:

Simplifying
16z2 + 3 = 16z

Reorder the terms:
3 + 16z2 = 16z

Solving
3 + 16z2 = 16z

Solving for variable 'z'.

Reorder the terms:
3 + -16z + 16z2 = 16z + -16z

Combine like terms: 16z + -16z = 0
3 + -16z + 16z2 = 0

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

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

Simplifying
1 + -4z = 0

Solving
1 + -4z = 0

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

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

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

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

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

Simplifying
z = 0.25
Subproblem 2
Set the factor '(3 + -4z)' equal to zero and attempt to solve:

Simplifying
3 + -4z = 0

Solving
3 + -4z = 0

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

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

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

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

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

Simplifying
z = 0.75
Solution
z = {0.25, 0.75}