8z^2+20z-48=0

Solution for 8z^2+20z-48=0 equation:

Simplifying
8z2 + 20z + -48 = 0

Reorder the terms:
-48 + 20z + 8z2 = 0

Solving
-48 + 20z + 8z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-12 + 5z + 2z2) = 0

Factor a trinomial.
4((-4 + -1z)(3 + -2z)) = 0

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

Simplifying
-4 + -1z = 0

Solving
-4 + -1z = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1z = 0 + 4

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

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

Divide each side by '-1'.
z = -4

Simplifying
z = -4
Subproblem 2
Set the factor '(3 + -2z)' equal to zero and attempt to solve:

Simplifying
3 + -2z = 0

Solving
3 + -2z = 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 + -2z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2z = 0 + -3
-2z = 0 + -3

Combine like terms: 0 + -3 = -3
-2z = -3

Divide each side by '-2'.
z = 1.5

Simplifying
z = 1.5
Solution
z = {-4, 1.5}