3z^2+2z-16=0

Solution for 3z^2+2z-16=0 equation:

Simplifying
3z2 + 2z + -16 = 0

Reorder the terms:
-16 + 2z + 3z2 = 0

Solving
-16 + 2z + 3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-8 + -3z)(2 + -1z) = 0

Subproblem 1
Set the factor '(-8 + -3z)' equal to zero and attempt to solve:

Simplifying
-8 + -3z = 0

Solving
-8 + -3z = 0

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

Add '8' to each side of the equation.
-8 + 8 + -3z = 0 + 8

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

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

Divide each side by '-3'.
z = -2.666666667

Simplifying
z = -2.666666667
Subproblem 2
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
Solution
z = {-2.666666667, 2}