7z^2-2z-5=0

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

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

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

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

Solving for variable 'z'.

Factor a trinomial.
(-5 + -7z)(1 + -1z) = 0

Subproblem 1
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
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 = {-0.7142857143, 1}