3z+6=4z^2+4z+1

Solution for 3z+6=4z^2+4z+1 equation:

Simplifying
3z + 6 = 4z2 + 4z + 1

Reorder the terms:
6 + 3z = 4z2 + 4z + 1

Reorder the terms:
6 + 3z = 1 + 4z + 4z2

Solving
6 + 3z = 1 + 4z + 4z2

Solving for variable 'z'.

Reorder the terms:
6 + -1 + 3z + -4z + -4z2 = 1 + 4z + 4z2 + -1 + -4z + -4z2

Combine like terms: 6 + -1 = 5
5 + 3z + -4z + -4z2 = 1 + 4z + 4z2 + -1 + -4z + -4z2

Combine like terms: 3z + -4z = -1z
5 + -1z + -4z2 = 1 + 4z + 4z2 + -1 + -4z + -4z2

Reorder the terms:
5 + -1z + -4z2 = 1 + -1 + 4z + -4z + 4z2 + -4z2

Combine like terms: 1 + -1 = 0
5 + -1z + -4z2 = 0 + 4z + -4z + 4z2 + -4z2
5 + -1z + -4z2 = 4z + -4z + 4z2 + -4z2

Combine like terms: 4z + -4z = 0
5 + -1z + -4z2 = 0 + 4z2 + -4z2
5 + -1z + -4z2 = 4z2 + -4z2

Combine like terms: 4z2 + -4z2 = 0
5 + -1z + -4z2 = 0

Factor a trinomial.
(1 + -1z)(5 + 4z) = 0

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

Simplifying
1 + -1z = 0

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

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

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

Divide each side by '-1'.
z = 1

Simplifying
z = 1
Subproblem 2
Set the factor '(5 + 4z)' equal to zero and attempt to solve:

Simplifying
5 + 4z = 0

Solving
5 + 4z = 0

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

Add '-5' to each side of the equation.
5 + -5 + 4z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4z = 0 + -5
4z = 0 + -5

Combine like terms: 0 + -5 = -5
4z = -5

Divide each side by '4'.
z = -1.25

Simplifying
z = -1.25
Solution
z = {1, -1.25}