4z^2+52z+48=0

Solution for 4z^2+52z+48=0 equation:

Simplifying
4z2 + 52z + 48 = 0

Reorder the terms:
48 + 52z + 4z2 = 0

Solving
48 + 52z + 4z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '4'.
4(12 + 13z + z2) = 0

Factor a trinomial.
4((12 + z)(1 + z)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(12 + z)' equal to zero and attempt to solve:

Simplifying
12 + z = 0

Solving
12 + z = 0

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

Add '-12' to each side of the equation.
12 + -12 + z = 0 + -12

Combine like terms: 12 + -12 = 0
0 + z = 0 + -12
z = 0 + -12

Combine like terms: 0 + -12 = -12
z = -12

Simplifying
z = -12
Subproblem 2
Set the factor '(1 + z)' equal to zero and attempt to solve:

Simplifying
1 + z = 0

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

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

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

Simplifying
z = -1
Solution
z = {-12, -1}