7z^2-20z-3=0

Solution for 7z^2-20z-3=0 equation:

Simplifying
7z2 + -20z + -3 = 0

Reorder the terms:
-3 + -20z + 7z2 = 0

Solving
-3 + -20z + 7z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-1 + -7z)(3 + -1z) = 0

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

Simplifying
-1 + -7z = 0

Solving
-1 + -7z = 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 + -7z = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -7z = 0 + 1
-7z = 0 + 1

Combine like terms: 0 + 1 = 1
-7z = 1

Divide each side by '-7'.
z = -0.1428571429

Simplifying
z = -0.1428571429
Subproblem 2
Set the factor '(3 + -1z)' equal to zero and attempt to solve:

Simplifying
3 + -1z = 0

Solving
3 + -1z = 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 + -1z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1z = 0 + -3
-1z = 0 + -3

Combine like terms: 0 + -3 = -3
-1z = -3

Divide each side by '-1'.
z = 3

Simplifying
z = 3
Solution
z = {-0.1428571429, 3}