5z^2+8z+3=0

Solution for 5z^2+8z+3=0 equation:

Simplifying
5z2 + 8z + 3 = 0

Reorder the terms:
3 + 8z + 5z2 = 0

Solving
3 + 8z + 5z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(1 + z)(3 + 5z) = 0

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

Simplifying
1 + z = 0

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

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

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

Simplifying
z = -1
Subproblem 2
Set the factor '(3 + 5z)' equal to zero and attempt to solve:

Simplifying
3 + 5z = 0

Solving
3 + 5z = 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 + 5z = 0 + -3

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

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

Divide each side by '5'.
z = -0.6

Simplifying
z = -0.6
Solution
z = {-1, -0.6}