20z^2+7z-6=0

Solution for 20z^2+7z-6=0 equation:

Simplifying
20z2 + 7z + -6 = 0

Reorder the terms:
-6 + 7z + 20z2 = 0

Solving
-6 + 7z + 20z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-3 + -4z)(2 + -5z) = 0

Subproblem 1
Set the factor '(-3 + -4z)' equal to zero and attempt to solve:

Simplifying
-3 + -4z = 0

Solving
-3 + -4z = 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 + -4z = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4z = 0 + 3
-4z = 0 + 3

Combine like terms: 0 + 3 = 3
-4z = 3

Divide each side by '-4'.
z = -0.75

Simplifying
z = -0.75
Subproblem 2
Set the factor '(2 + -5z)' equal to zero and attempt to solve:

Simplifying
2 + -5z = 0

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

Combine like terms: 2 + -2 = 0
0 + -5z = 0 + -2
-5z = 0 + -2

Combine like terms: 0 + -2 = -2
-5z = -2

Divide each side by '-5'.
z = 0.4

Simplifying
z = 0.4
Solution
z = {-0.75, 0.4}