7z^2-2z-9=0

Solution for 7z^2-2z-9=0 equation:

Simplifying
7z2 + -2z + -9 = 0

Reorder the terms:
-9 + -2z + 7z2 = 0

Solving
-9 + -2z + 7z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-1 + -1z)(9 + -7z) = 0

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

Simplifying
-1 + -1z = 0

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

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

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

Divide each side by '-1'.
z = -1

Simplifying
z = -1
Subproblem 2
Set the factor '(9 + -7z)' equal to zero and attempt to solve:

Simplifying
9 + -7z = 0

Solving
9 + -7z = 0

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

Add '-9' to each side of the equation.
9 + -9 + -7z = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -7z = 0 + -9
-7z = 0 + -9

Combine like terms: 0 + -9 = -9
-7z = -9

Divide each side by '-7'.
z = 1.285714286

Simplifying
z = 1.285714286
Solution
z = {-1, 1.285714286}