4z^2+1=4z

Solution for 4z^2+1=4z equation:

Simplifying
4z2 + 1 = 4z

Reorder the terms:
1 + 4z2 = 4z

Solving
1 + 4z2 = 4z

Solving for variable 'z'.

Reorder the terms:
1 + -4z + 4z2 = 4z + -4z

Combine like terms: 4z + -4z = 0
1 + -4z + 4z2 = 0

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

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

Simplifying
1 + -2z = 0

Solving
1 + -2z = 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 + -2z = 0 + -1

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

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

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

Simplifying
z = 0.5
Subproblem 2
Set the factor '(1 + -2z)' equal to zero and attempt to solve:

Simplifying
1 + -2z = 0

Solving
1 + -2z = 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 + -2z = 0 + -1

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

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

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

Simplifying
z = 0.5
Solution
z = {0.5, 0.5}