8z^2+14z=-5

Solution for 8z^2+14z=-5 equation:

Simplifying
8z2 + 14z = -5

Reorder the terms:
14z + 8z2 = -5

Solving
14z + 8z2 = -5

Solving for variable 'z'.

Reorder the terms:
5 + 14z + 8z2 = -5 + 5

Combine like terms: -5 + 5 = 0
5 + 14z + 8z2 = 0

Factor a trinomial.
(5 + 4z)(1 + 2z) = 0

Subproblem 1
Set the factor '(5 + 4z)' equal to zero and attempt to solve:

Simplifying
5 + 4z = 0

Solving
5 + 4z = 0

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

Add '-5' to each side of the equation.
5 + -5 + 4z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4z = 0 + -5
4z = 0 + -5

Combine like terms: 0 + -5 = -5
4z = -5

Divide each side by '4'.
z = -1.25

Simplifying
z = -1.25
Subproblem 2
Set the factor '(1 + 2z)' equal to zero and attempt to solve:

Simplifying
1 + 2z = 0

Solving
1 + 2z = 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 + 2z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2z = 0 + -1
2z = 0 + -1

Combine like terms: 0 + -1 = -1
2z = -1

Divide each side by '2'.
z = -0.5

Simplifying
z = -0.5
Solution
z = {-1.25, -0.5}