3z^2+8z+2=5

Solution for 3z^2+8z+2=5 equation:

Simplifying
3z2 + 8z + 2 = 5

Reorder the terms:
2 + 8z + 3z2 = 5

Solving
2 + 8z + 3z2 = 5

Solving for variable 'z'.

Reorder the terms:
2 + -5 + 8z + 3z2 = 5 + -5

Combine like terms: 2 + -5 = -3
-3 + 8z + 3z2 = 5 + -5

Combine like terms: 5 + -5 = 0
-3 + 8z + 3z2 = 0

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

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

Simplifying
-3 + -1z = 0

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

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

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

Divide each side by '-1'.
z = -3

Simplifying
z = -3
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 = {-3, 0.3333333333}