9z^2+2z-7=0

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

Simplifying
9z2 + 2z + -7 = 0

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

Solving
-7 + 2z + 9z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-1 + -1z)(7 + -9z) = 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 '(7 + -9z)' equal to zero and attempt to solve:

Simplifying
7 + -9z = 0

Solving
7 + -9z = 0

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

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

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

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

Divide each side by '-9'.
z = 0.7777777778

Simplifying
z = 0.7777777778
Solution
z = {-1, 0.7777777778}