7z^2+26z+15=0

Solution for 7z^2+26z+15=0 equation:

Simplifying
7z2 + 26z + 15 = 0

Reorder the terms:
15 + 26z + 7z2 = 0

Solving
15 + 26z + 7z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(3 + z)(5 + 7z) = 0

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

Simplifying
3 + z = 0

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

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

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

Simplifying
z = -3
Subproblem 2
Set the factor '(5 + 7z)' equal to zero and attempt to solve:

Simplifying
5 + 7z = 0

Solving
5 + 7z = 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 + 7z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 7z = 0 + -5
7z = 0 + -5

Combine like terms: 0 + -5 = -5
7z = -5

Divide each side by '7'.
z = -0.7142857143

Simplifying
z = -0.7142857143
Solution
z = {-3, -0.7142857143}