3z^2+8z+6=9

Solution for 3z^2+8z+6=9 equation:

Simplifying
3z2 + 8z + 6 = 9

Reorder the terms:
6 + 8z + 3z2 = 9

Solving
6 + 8z + 3z2 = 9

Solving for variable 'z'.

Reorder the terms:
6 + -9 + 8z + 3z2 = 9 + -9

Combine like terms: 6 + -9 = -3
-3 + 8z + 3z2 = 9 + -9

Combine like terms: 9 + -9 = 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}