3z^2+46z+15=0

Solution for 3z^2+46z+15=0 equation:

Simplifying
3z2 + 46z + 15 = 0

Reorder the terms:
15 + 46z + 3z2 = 0

Solving
15 + 46z + 3z2 = 0

Solving for variable 'z'.

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

Subproblem 1
Set the factor '(15 + z)' equal to zero and attempt to solve:

Simplifying
15 + z = 0

Solving
15 + z = 0

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

Add '-15' to each side of the equation.
15 + -15 + z = 0 + -15

Combine like terms: 15 + -15 = 0
0 + z = 0 + -15
z = 0 + -15

Combine like terms: 0 + -15 = -15
z = -15

Simplifying
z = -15
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 = {-15, -0.3333333333}