7z^2+17z+10=0

Solution for 7z^2+17z+10=0 equation:

Simplifying
7z2 + 17z + 10 = 0

Reorder the terms:
10 + 17z + 7z2 = 0

Solving
10 + 17z + 7z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(10 + 7z)(1 + z) = 0

Subproblem 1
Set the factor '(10 + 7z)' equal to zero and attempt to solve:

Simplifying
10 + 7z = 0

Solving
10 + 7z = 0

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

Add '-10' to each side of the equation.
10 + -10 + 7z = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 7z = 0 + -10
7z = 0 + -10

Combine like terms: 0 + -10 = -10
7z = -10

Divide each side by '7'.
z = -1.428571429

Simplifying
z = -1.428571429
Subproblem 2
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
Solution
z = {-1.428571429, -1}