3z^2+5z+1=3

Solution for 3z^2+5z+1=3 equation:

Simplifying
3z2 + 5z + 1 = 3

Reorder the terms:
1 + 5z + 3z2 = 3

Solving
1 + 5z + 3z2 = 3

Solving for variable 'z'.

Reorder the terms:
1 + -3 + 5z + 3z2 = 3 + -3

Combine like terms: 1 + -3 = -2
-2 + 5z + 3z2 = 3 + -3

Combine like terms: 3 + -3 = 0
-2 + 5z + 3z2 = 0

Factor a trinomial.
(-2 + -1z)(1 + -3z) = 0

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

Simplifying
-2 + -1z = 0

Solving
-2 + -1z = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1z = 0 + 2

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

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

Divide each side by '-1'.
z = -2

Simplifying
z = -2
Subproblem 2
Set the factor '(1 + -3z)' equal to zero and attempt to solve:

Simplifying
1 + -3z = 0

Solving
1 + -3z = 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 + -3z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3z = 0 + -1
-3z = 0 + -1

Combine like terms: 0 + -1 = -1
-3z = -1

Divide each side by '-3'.
z = 0.3333333333

Simplifying
z = 0.3333333333
Solution
z = {-2, 0.3333333333}