20z^2+7z-3=0

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

Simplifying
20z2 + 7z + -3 = 0

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

Solving
-3 + 7z + 20z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-3 + -5z)(1 + -4z) = 0

Subproblem 1
Set the factor '(-3 + -5z)' equal to zero and attempt to solve:

Simplifying
-3 + -5z = 0

Solving
-3 + -5z = 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 + -5z = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5z = 0 + 3
-5z = 0 + 3

Combine like terms: 0 + 3 = 3
-5z = 3

Divide each side by '-5'.
z = -0.6

Simplifying
z = -0.6
Subproblem 2
Set the factor '(1 + -4z)' equal to zero and attempt to solve:

Simplifying
1 + -4z = 0

Solving
1 + -4z = 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 + -4z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4z = 0 + -1
-4z = 0 + -1

Combine like terms: 0 + -1 = -1
-4z = -1

Divide each side by '-4'.
z = 0.25

Simplifying
z = 0.25
Solution
z = {-0.6, 0.25}