6z^2-28z-48=0

Solution for 6z^2-28z-48=0 equation:

Simplifying
6z2 + -28z + -48 = 0

Reorder the terms:
-48 + -28z + 6z2 = 0

Solving
-48 + -28z + 6z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-24 + -14z + 3z2) = 0

Factor a trinomial.
2((-4 + -3z)(6 + -1z)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + -3z)' equal to zero and attempt to solve:

Simplifying
-4 + -3z = 0

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

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

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

Divide each side by '-3'.
z = -1.333333333

Simplifying
z = -1.333333333
Subproblem 2
Set the factor '(6 + -1z)' equal to zero and attempt to solve:

Simplifying
6 + -1z = 0

Solving
6 + -1z = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1z = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1z = 0 + -6
-1z = 0 + -6

Combine like terms: 0 + -6 = -6
-1z = -6

Divide each side by '-1'.
z = 6

Simplifying
z = 6
Solution
z = {-1.333333333, 6}