12z^2+80z+48=0

Solution for 12z^2+80z+48=0 equation:

Simplifying
12z2 + 80z + 48 = 0

Reorder the terms:
48 + 80z + 12z2 = 0

Solving
48 + 80z + 12z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '4'.
4(12 + 20z + 3z2) = 0

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

Ignore the factor 4.
Subproblem 1
Set the factor '(6 + z)' equal to zero and attempt to solve:

Simplifying
6 + z = 0

Solving
6 + z = 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 + z = 0 + -6

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

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

Simplifying
z = -6
Subproblem 2
Set the factor '(2 + 3z)' equal to zero and attempt to solve:

Simplifying
2 + 3z = 0

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

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

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

Divide each side by '3'.
z = -0.6666666667

Simplifying
z = -0.6666666667
Solution
z = {-6, -0.6666666667}