7z^2-5z-2=0

Solution for 7z^2-5z-2=0 equation:

Simplifying
7z2 + -5z + -2 = 0

Reorder the terms:
-2 + -5z + 7z2 = 0

Solving
-2 + -5z + 7z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-2 + -7z)(1 + -1z) = 0

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

Simplifying
-2 + -7z = 0

Solving
-2 + -7z = 0

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

Add '2' to each side of the equation.
-2 + 2 + -7z = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -7z = 0 + 2
-7z = 0 + 2

Combine like terms: 0 + 2 = 2
-7z = 2

Divide each side by '-7'.
z = -0.2857142857

Simplifying
z = -0.2857142857
Subproblem 2
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
Solution
z = {-0.2857142857, 1}